Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Videos
Question
Chapter 4.1, Problem 51E
To determine
To graph: The functions
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A boat is 15 ft away from a point perpendicular to the shoreline. A
person stands at a point down the shoreline so that a 65° angle
is formed between the closest point to the boat, the person, and
the boat. How far is the person from the boat? Round your
answer to the nearest tenth of a foot. Show your work.
boat
15 ft
d
65°
person
2. Find the value of x in the triangle. Round your answer to the
nearest tenth of a degree. Show your work.
8
15
Use the equation x+2= √3x+10 to answer these questions.
(a) What is the solution to the equation?
(b) What is the extraneous solution? Why?
(c) In general, what is an extraneous solution?
Chapter 4 Solutions
Algebra and Trigonometry (6th Edition)
Ch. 4.1 - Fill in each blank so that the resulting statement...Ch. 4.1 - The graph of the exponential function f with base...Ch. 4.1 - 3. The value that approaches as n gets larger and...Ch. 4.1 - Consider the compound interest formula...Ch. 4.1 - 5. If compound interest is paid twice a year, we...Ch. 4.1 - In Exercises 110, approximate each number using a...Ch. 4.1 - In Exercises 1-10, approximate each number using a...Ch. 4.1 - In Exercises 1-10, approximate each number using a...Ch. 4.1 - In Exercises 1-10, approximate each number using a...Ch. 4.1 - In Exercises 1-10, approximate each number using a...
Ch. 4.1 - In Exercises 1-10, approximate each number using a...Ch. 4.1 - In Exercises 1-10, approximate each number using a...Ch. 4.1 - In Exercises 1-10, approximate each number using a...Ch. 4.1 - In Exercises 1-10, approximate each number using a...Ch. 4.1 - In Exercises 1-10, approximate each number using a...Ch. 4.1 - In Exercises 11-I8, graph each function by making...Ch. 4.1 - In Exercises 11-18, graph each function by making...Ch. 4.1 - In Exercises 11-18, graph each function by making...Ch. 4.1 - In Exercises 11-18, graph each function by making...Ch. 4.1 - In Exercises 11-18, graph each function by making...Ch. 4.1 - In Exercises 11-18, graph each function by making...Ch. 4.1 - In Exercises 11-18, graph each function by making...Ch. 4.1 - In Exercises 11-18,graph each function by making a...Ch. 4.1 - In Exercises 19-24, the graph of an exponential...Ch. 4.1 - In Exercises 19-24, the graph of an exponential...Ch. 4.1 - In Exercises 19-24, the graph of an exponential...Ch. 4.1 - In Exercises 19-24, the graph of an exponential...Ch. 4.1 - In Exercises 19-24, the graph of an exponential...Ch. 4.1 - In Exercises 19-24, the graph of an exponential...Ch. 4.1 - In Exercises 25-34, begin by graphing f(x)=2x ....Ch. 4.1 - In Exercises 25-34, begin by graphing . Then use...Ch. 4.1 - In Exercises 25-34, begin by graphing . Then use...Ch. 4.1 - In Exercises 25-34, begin by graphing f(x)=2x ....Ch. 4.1 - In Exercises 25-34, begin by graphing f(x)=2x ....Ch. 4.1 - In Exercises 25-34, begin by graphing . Then use...Ch. 4.1 - In Exercises 25-34, begin by graphing f(x)=2x ....Ch. 4.1 - In Exercises 25-34, begin by graphing . Then use...Ch. 4.1 - Prob. 33ECh. 4.1 - In Exercises 25-34, begin by graphing f(x)=2x....Ch. 4.1 - The figure shows the graph of . In Exercises...Ch. 4.1 - The figure shows the graph of . In Exercises...Ch. 4.1 - The figure shows the graph of f(x)=c4 . In...Ch. 4.1 - The figure shows the graph of f(x)=c4 . In...Ch. 4.1 - The figure shows the graph of . In Exercises...Ch. 4.1 - The figure shows the graph of . In Exercises...Ch. 4.1 - The figure shows the graph of . In Exercises...Ch. 4.1 - The figure shows the graph of . In Exercises...Ch. 4.1 - The figure shows the graph of f(x)=c4 . In...Ch. 4.1 - The figure shows the graph of . In Exercises...Ch. 4.1 - The figure shows the graph of . In Exercises...Ch. 4.1 - The figure shows the graph of f(x)=c4 . In...Ch. 4.1 - Prob. 47ECh. 4.1 - Prob. 48ECh. 4.1 - In Exercises 47-52, graph functions f and g in the...Ch. 4.1 - Prob. 50ECh. 4.1 - Prob. 51ECh. 4.1 - Prob. 52ECh. 4.1 - Use the compound interest formulas A=P(1+rn)nt and...Ch. 4.1 - Prob. 54ECh. 4.1 - Use the compound interest formulas A=P(1+rn)nt and...Ch. 4.1 - Prob. 56ECh. 4.1 - Prob. 57ECh. 4.1 - Prob. 58ECh. 4.1 - Prob. 59ECh. 4.1 - Prob. 60ECh. 4.1 - In Exercises 61-64, give the equation of each...Ch. 4.1 - In Exercises 61-64, give the equation of each...Ch. 4.1 - In Exercises 61-64, give the equation of each...Ch. 4.1 - In Exercises 61-64, give the equation of each...Ch. 4.1 - Use a calculator with a key or a key to solve...Ch. 4.1 - Prob. 66ECh. 4.1 - Prob. 67ECh. 4.1 - Prob. 68ECh. 4.1 - Prob. 69ECh. 4.1 - Use a calculator with a key or a key to solve...Ch. 4.1 - Prob. 71ECh. 4.1 - Prob. 72ECh. 4.1 - Use a calculator with on yx key to solve Exercises...Ch. 4.1 - Prob. 74ECh. 4.1 - Prob. 75ECh. 4.1 - Prob. 76ECh. 4.1 - What is an exponential function?Ch. 4.1 - What is the natural exponential function?Ch. 4.1 - Prob. 79ECh. 4.1 - 80. Describe how you could use the graph of to...Ch. 4.1 - 81. You have $10,000 to invest. One bank pays 5%...Ch. 4.1 - a. Graph y=er and y=1+x+x22 rectangle. b. Graph...Ch. 4.1 - Prob. 83ECh. 4.1 - Prob. 84ECh. 4.1 - Make Sense? In Exercises 83-86, determine whether...Ch. 4.1 - Prob. 86ECh. 4.1 - Prob. 87ECh. 4.1 - Prob. 88ECh. 4.1 - In Exercises 87-90, determine whether each...Ch. 4.1 - In Exercises 87-90, determine whether each...Ch. 4.1 - 91. The graphs labeled (a)-(d) in the figure...Ch. 4.1 - Prob. 92ECh. 4.1 - Prob. 93ECh. 4.1 - Prob. 94ECh. 4.1 - Prob. 95ECh. 4.1 - Solve and graph the solution set on a number line:...Ch. 4.1 - Exercises 97-99 will help you prepare for the...Ch. 4.1 - Prob. 98ECh. 4.1 - Exercises 97-99 will help you prepare for the...Ch. 4.2 - 1. is equivalent to the exponential...Ch. 4.2 - The function f(x)=logbx is the _________ function...Ch. 4.2 - 3. ________
Ch. 4.2 - 4.
Ch. 4.2 - logbbx=Ch. 4.2 - blogbx=Ch. 4.2 - Fill in each blank so that the resulting statement...Ch. 4.2 - Fill in each blank so that the resulting statement...Ch. 4.2 - Fill in each blank so that the resulting statement...Ch. 4.2 - Fill in each blank so that the resulting statement...Ch. 4.2 - Fill in each blank so that the resulting statement...Ch. 4.2 - Fill in each blank so that the resulting statement...Ch. 4.2 - Fill in each blank so that the resulting statement...Ch. 4.2 - Fill in each blank so that the resulting statement...Ch. 4.2 - Fill in each blank so that the resulting statement...Ch. 4.2 - In Exercises 1-8, write each equation in its...Ch. 4.2 - In Exercises 1-8, write each equation in its...Ch. 4.2 - In Exercises 1-8, write each equation in its...Ch. 4.2 - In Exercises 1-8, write each equation in its...Ch. 4.2 - In Exercises 1-8, write each equation in its...Ch. 4.2 - In Exercises 1-8, write each equation in its...Ch. 4.2 - In Exercises 1-8, write each equation in its...Ch. 4.2 - In Exercises 1-8, write each equation in its...Ch. 4.2 - In Exercises 9-20, write each equation in its...Ch. 4.2 - In Exercises 9-20, write each equation in its...Ch. 4.2 - In Exercises 9-20, write each equation in its...Ch. 4.2 - In Exercises 9-20, write each equation in its...Ch. 4.2 - In Exercises 9-20, write each equation in its...Ch. 4.2 - In Exercises 9-20, write each equation in its...Ch. 4.2 - In Exercises 9-20, write each equation in its...Ch. 4.2 - In Exercises 9-20, write each equation in its...Ch. 4.2 - In Exercises 9-20, write each equation in its...Ch. 4.2 - In Exercises 9-20, write each equation in its...Ch. 4.2 - In Exercises 9-20, write each equation in its...Ch. 4.2 - In Exercises 9-20, write each equation in its...Ch. 4.2 - In Exercises 21-42, evaluate each expression...Ch. 4.2 - In Exercises 21-42, evaluate each expression...Ch. 4.2 - In Exercises 21-42, evaluate each expression...Ch. 4.2 - In Exercises 21-42, evaluate each expression...Ch. 4.2 - In Exercises 21-42, evaluate each expression...Ch. 4.2 - In Exercises 21-42, evaluate each expression...Ch. 4.2 - 27.
In Exercises 21-42, evaluate each expression...Ch. 4.2 - In Exercises 21-42, evaluate each expression...Ch. 4.2 - In Exercises 21-42, evaluate each expression...Ch. 4.2 - In Exercises 21-42, evaluate each expression...Ch. 4.2 - In Exercises 21-42, evaluate each expression...Ch. 4.2 - In Exercises 21-42, evaluate each expression...Ch. 4.2 - In Exercises 21-42, evaluate each expression...Ch. 4.2 - In Exercises 21-42, evaluate each expression...Ch. 4.2 - In Exercises 21-42, evaluate each expression...Ch. 4.2 - In Exercises 21-42, evaluate each expression...Ch. 4.2 - In Exercises 21-42, evaluate each expression...Ch. 4.2 - In Exercises 21-42, evaluate each expression...Ch. 4.2 - In Exercises 21-42, evaluate each expression...Ch. 4.2 - In Exercises 21-42, evaluate each expression...Ch. 4.2 - In Exercises 21- 42, evaluate each expression...Ch. 4.2 - In Exercises 21- 42, evaluate each expression...Ch. 4.2 - Graph f(x)=4x and g(x)=log4x in the same...Ch. 4.2 - Graph f(x)=5x and g(x)=log5x in the same...Ch. 4.2 - Graph f(x)=(12)x and g(x)=log(12)x in the same...Ch. 4.2 - 16. Graph and in the same rectangular coordinate...Ch. 4.2 - In Exercises 47-52, the graph of a logarithmic...Ch. 4.2 - In Exercises 47-52, the graph of a logarithmic...Ch. 4.2 - In Exercises 47-52, the graph of a logarithmic...Ch. 4.2 - In Exercises 47-52, the graph of a logarithmic...Ch. 4.2 - In Exercises 47-52, the graph of a logarithmic...Ch. 4.2 - In Exercises 47-52, the graph of a logarithmic...Ch. 4.2 - In Exercises 53-58, begin by graphing...Ch. 4.2 - In Exercises 53-58, begin by graphing f(x)=log2x ....Ch. 4.2 - Prob. 55ECh. 4.2 - Prob. 56ECh. 4.2 - In Exercises 53-58, begin by graphing f(x)=log2x....Ch. 4.2 - Prob. 58ECh. 4.2 - Prob. 59ECh. 4.2 - The figure shows the graph of . In Exercises...Ch. 4.2 - The figure shows the graph of f(x)=logx . In...Ch. 4.2 - Prob. 62ECh. 4.2 - Prob. 63ECh. 4.2 - Prob. 64ECh. 4.2 - The figure shows the graph of . In Exercises...Ch. 4.2 - Prob. 66ECh. 4.2 - Prob. 67ECh. 4.2 - Prob. 68ECh. 4.2 - The figure shows the graph of f(x)=lnx . In...Ch. 4.2 - Prob. 70ECh. 4.2 - The figure shows the graph of f(x)=lnx . In...Ch. 4.2 - Prob. 72ECh. 4.2 - The figure shows the graph of f(x)=lnx . In...Ch. 4.2 - Prob. 74ECh. 4.2 - In Exercises 75-80, find the domain of each...Ch. 4.2 - In Exercises 75-80, find the domain of each...Ch. 4.2 - In Exercises 75-80, find the domain of each...Ch. 4.2 - In Exercises 75-80, find the domain of each...Ch. 4.2 - In Exercises 75-80, find the domain of each...Ch. 4.2 - f(x)=ln(x7)2Ch. 4.2 - log 100Ch. 4.2 - In Exercises 81-100, evaluate or simplify each...Ch. 4.2 - In Exercises 81-100, evaluate or simplify each...Ch. 4.2 - 84. log 108
Ch. 4.2 - 85. 10 log 33
Ch. 4.2 - 86. 10 log 53
Ch. 4.2 - 87. In 1
Ch. 4.2 - 88. In e
Ch. 4.2 - In e6Ch. 4.2 - In e7Ch. 4.2 - ln1e6Ch. 4.2 - In Exercises 81-100, evaluate or simplify each...Ch. 4.2 - In Exercises 81-100, evaluate or simplify each...Ch. 4.2 - In Exercises 81-100, evaluate or simplify each...Ch. 4.2 - In Exercises 81-100, evaluate or simplify each...Ch. 4.2 - In Exercises 81-100, evaluate or simplify each...Ch. 4.2 - In Exercises 81-100, evaluate or simplify each...Ch. 4.2 - In Exercises 81-100, evaluate or simplify each...Ch. 4.2 - In Exercises 81-100, evaluate or simplify each...Ch. 4.2 - In Exercises 81-100, evaluate or simplify each...Ch. 4.2 - In Exercises 101-104, write each equation in its...Ch. 4.2 - Prob. 102ECh. 4.2 - Prob. 103ECh. 4.2 - Prob. 104ECh. 4.2 - In Exercises 105-108, evaluate each expression...Ch. 4.2 - Prob. 106ECh. 4.2 - Prob. 107ECh. 4.2 - Prob. 108ECh. 4.2 - In Exercises 109-112, find the domain of each...Ch. 4.2 - Prob. 110ECh. 4.2 - Prob. 111ECh. 4.2 - Prob. 112ECh. 4.2 - The percentage of adult height attained by a girl...Ch. 4.2 - The percentage of adult height attained by a girl...Ch. 4.2 - 115. The function
models the wives' weekly...Ch. 4.2 - The bar graph shows the average number of hours...Ch. 4.2 - The loudness level of a sound, D, in decibels, is...Ch. 4.2 - The loudness level of a sound, D. in decibels, is...Ch. 4.2 - Prob. 119ECh. 4.2 - Prob. 120ECh. 4.2 - What question can be asked to help evaluate log3...Ch. 4.2 - Prob. 122ECh. 4.2 - 123. Describe the following property using words:...Ch. 4.2 - Prob. 124ECh. 4.2 - Prob. 125ECh. 4.2 - Prob. 126ECh. 4.2 - 127. Suppose that a girl is 4 feet 6 inches at age...Ch. 4.2 - Prob. 128ECh. 4.2 - Prob. 129ECh. 4.2 - Prob. 130ECh. 4.2 - Prob. 131ECh. 4.2 - Prob. 132ECh. 4.2 - Prob. 133ECh. 4.2 - Prob. 134ECh. 4.2 - Prob. 135ECh. 4.2 - Prob. 136ECh. 4.2 - Prob. 137ECh. 4.2 - Prob. 138ECh. 4.2 - Prob. 139ECh. 4.2 - Prob. 140ECh. 4.2 - Prob. 141ECh. 4.2 - Prob. 142ECh. 4.2 - Prob. 143ECh. 4.2 - Prob. 144ECh. 4.2 - Prob. 145ECh. 4.2 - Prob. 146ECh. 4.2 - Prob. 147ECh. 4.2 - Prob. 148ECh. 4.2 - Prob. 149ECh. 4.2 - Prob. 150ECh. 4.2 - Prob. 151ECh. 4.2 - Prob. 152ECh. 4.3 - Fill in each blank so that the resulting statement...Ch. 4.3 - Fill in each blank so that the resulting statement...Ch. 4.3 - Fill in each blank so that the resulting statement...Ch. 4.3 - Fill in each blank so that the resulting statement...Ch. 4.3 - In Exercises 1-40, use properties of logarithms to...Ch. 4.3 - Prob. 2ECh. 4.3 - In Exercises 1-40, use properties of logarithms to...Ch. 4.3 - In Exercises 1-40, use properties of logarithms to...Ch. 4.3 - In Exercises 1-40, use properties of logarithms to...Ch. 4.3 - In Exercises 1-40, use properties of logarithms to...Ch. 4.3 - In Exercises 1-40, use properties of logarithms to...Ch. 4.3 - In Exercises 1-40, use properties of logarithms to...Ch. 4.3 - In Exercises 1-40, use properties of logarithms to...Ch. 4.3 - In Exercises 1-40, use properties of logarithms to...Ch. 4.3 - In Exercises 1-40, use properties of logarithms to...Ch. 4.3 - In Exercises 1-40, use properties of logarithms to...Ch. 4.3 - In Exercises 1-40, use properties of logarithms to...Ch. 4.3 - Prob. 14ECh. 4.3 - In Exercises 1-40, use properties of logarithms to...Ch. 4.3 - Prob. 16ECh. 4.3 - In Exercises 1-40, use properties of logarithms to...Ch. 4.3 - Prob. 18ECh. 4.3 - In Exercises 1-40, use properties of logarithms to...Ch. 4.3 - Prob. 20ECh. 4.3 - In Exercises 1-40, use properties of logarithms to...Ch. 4.3 - Prob. 22ECh. 4.3 - In Exercises 1-40, use properties of logarithms to...Ch. 4.3 - Prob. 24ECh. 4.3 - In Exercises 1-40, use properties of logarithms to...Ch. 4.3 - Prob. 26ECh. 4.3 - In Exercises 1-40, use properties of logarithms to...Ch. 4.3 - Prob. 28ECh. 4.3 - In Exercises 1-40, use properties of logarithms to...Ch. 4.3 - In Exercises 1-40, use properties of logarithms to...Ch. 4.3 - In Exercises 1-40, use properties of logarithms to...Ch. 4.3 - In Exercises 1-40, use properties of logarithms to...Ch. 4.3 - In Exercises 1-40, use properties of logarithms to...Ch. 4.3 - In Exercises 1-40, use properties of logarithms to...Ch. 4.3 - In Exercises 1-40, use properties of logarithms to...Ch. 4.3 - In Exercises 1-40, use properties of logarithms to...Ch. 4.3 - In Exercises 1-40, use properties of logarithms to...Ch. 4.3 - In Exercises 1-40, use properties of logarithms to...Ch. 4.3 - In Exercises 1-40, use properties of logarithms to...Ch. 4.3 - In Exercises 1-40, use properties of logarithms to...Ch. 4.3 - In Exercises 41-70, use properties of logarithms...Ch. 4.3 - In Exercises 41-70, use properties of logarithms...Ch. 4.3 - In Exercises 41-70, use properties of logarithms...Ch. 4.3 - In Exercises 41-70, use properties of logarithms...Ch. 4.3 - In Exercises 41-70, use properties of logarithms...Ch. 4.3 - In Exercises 41-70, use properties of logarithms...Ch. 4.3 - In Exercises 41-70, use properties of logarithms...Ch. 4.3 - In Exercises 41-70, use properties of logarithms...Ch. 4.3 - In Exercises 41-70, use properties of logarithms...Ch. 4.3 - In Exercises 41-70, use properties of logarithms...Ch. 4.3 - In Exercises 41-70, use properties of logarithms...Ch. 4.3 - In Exercises 41-70, use properties of logarithms...Ch. 4.3 - In Exercises 41-70, use properties of logarithms...Ch. 4.3 - In Exercises 41-70, use properties of logarithms...Ch. 4.3 - In Exercises 41-70, use properties of logarithms...Ch. 4.3 - In Exercises 41-70, use properties of logarithms...Ch. 4.3 - In Exercises 41-70, use properties of logarithms...Ch. 4.3 - In Exercises 41-70, use properties of logarithms...Ch. 4.3 - In Exercises 41-70, use properties of logarithms...Ch. 4.3 - In Exercises 41-70, use properties of logarithms...Ch. 4.3 - In Exercises 41-70, use properties of logarithms...Ch. 4.3 - In Exercises -41-70, use properties of logarithms...Ch. 4.3 - In Exercises 41-70, use properties of logarithms...Ch. 4.3 - Prob. 64ECh. 4.3 - Prob. 65ECh. 4.3 - Prob. 66ECh. 4.3 - In Exercises 41-70, use properties of logarithms...Ch. 4.3 - In Exercises 41-70, use properties of logarithms...Ch. 4.3 - In Exercises 41-70, use properties of logarithms...Ch. 4.3 - In Exercises 41-70, use properties of logarithms...Ch. 4.3 - In Exercises 71–78, use common logarithms or...Ch. 4.3 - Prob. 72ECh. 4.3 - Prob. 73ECh. 4.3 - Prob. 74ECh. 4.3 - In Exercises 71-78, use common logarithms or...Ch. 4.3 - Prob. 76ECh. 4.3 - Prob. 77ECh. 4.3 - Prob. 78ECh. 4.3 - In Exercises 79-82, use a graphing utility and the...Ch. 4.3 - In Exercises 79-82, use a graphing utility and the...Ch. 4.3 - In Exercises 79-82, use a graphing utility and the...Ch. 4.3 - In Exercises 79-82, use a graphing utility and the...Ch. 4.3 - In Exercises 83-88, let and . Write each...Ch. 4.3 - Prob. 84ECh. 4.3 - In Exercises 83-88, let and . Write each...Ch. 4.3 - Prob. 86ECh. 4.3 - Prob. 87ECh. 4.3 - Prob. 88ECh. 4.3 - In Exercises 89-102, determine whether each...Ch. 4.3 - In Exercises 89-102, determine whether each...Ch. 4.3 - In Exercises 89-102, determine whether each...Ch. 4.3 - In Exercises 89-102, determine whether each...Ch. 4.3 - In Exercises 89-102, determine whether each...Ch. 4.3 - Prob. 94ECh. 4.3 - Prob. 95ECh. 4.3 - Prob. 96ECh. 4.3 - Prob. 97ECh. 4.3 - Prob. 98ECh. 4.3 - Prob. 99ECh. 4.3 - Prob. 100ECh. 4.3 - In Exercises 89–102, determine whether each...Ch. 4.3 - Prob. 102ECh. 4.3 - 103. The loudness level of a sound can be...Ch. 4.3 - Prob. 104ECh. 4.3 - Prob. 105ECh. 4.3 - Prob. 106ECh. 4.3 - Prob. 107ECh. 4.3 - Prob. 108ECh. 4.3 - Prob. 109ECh. 4.3 - Prob. 110ECh. 4.3 - 111. You overhear a student talking about a...Ch. 4.3 - Prob. 112ECh. 4.3 - Prob. 113ECh. 4.3 - Prob. 114ECh. 4.3 - Prob. 115ECh. 4.3 - Prob. 116ECh. 4.3 - Prob. 117ECh. 4.3 - Prob. 118ECh. 4.3 - Disprove each statement in Exercises 116-120 by a...Ch. 4.3 - Prob. 120ECh. 4.3 - Prob. 121ECh. 4.3 - Prob. 122ECh. 4.3 - Prob. 123ECh. 4.3 - Prob. 124ECh. 4.3 - Prob. 125ECh. 4.3 - Prob. 126ECh. 4.3 - Prob. 127ECh. 4.3 - Prob. 128ECh. 4.3 - Prob. 129ECh. 4.3 - Prob. 130ECh. 4.3 - Prob. 131ECh. 4.3 - If f(x) - logb x, show that...Ch. 4.3 - Prob. 133ECh. 4.3 - Prob. 134ECh. 4.3 - Prob. 135ECh. 4.3 - Prob. 136ECh. 4.3 - Prob. 137ECh. 4.3 - Prob. 138ECh. 4.3 - Prob. 139ECh. 4.4 - If bM = bN, then__________Ch. 4.4 - If 24x1=27, then _______ =7.Ch. 4.4 - Prob. 3CVCCh. 4.4 - Prob. 4CVCCh. 4.4 - Prob. 5CVCCh. 4.4 - Prob. 6CVCCh. 4.4 - Prob. 7CVCCh. 4.4 - Prob. 8CVCCh. 4.4 - Prob. 9CVCCh. 4.4 - Prob. 10CVCCh. 4.4 - Prob. 11CVCCh. 4.4 - Solve each exponential equation in Exercises 1-22...Ch. 4.4 - Prob. 2ECh. 4.4 - Solve each exponential equation in Exercises 1-22...Ch. 4.4 - Prob. 4ECh. 4.4 - Solve each exponential equation in Exercises 1-22...Ch. 4.4 - Prob. 6ECh. 4.4 - Solve each exponential equation in Exercises 1-22...Ch. 4.4 - Solve each exponential equation in Exercises 1-22...Ch. 4.4 - Solve each exponential equation in Exercises 1-22...Ch. 4.4 - Solve each exponential equation in Exercises 1-22...Ch. 4.4 - Solve each exponential equation in Exercises 1-22...Ch. 4.4 - Prob. 12ECh. 4.4 - Prob. 13ECh. 4.4 - Prob. 14ECh. 4.4 - Solve each exponential equation in Exercises 1-22...Ch. 4.4 - Prob. 16ECh. 4.4 - Prob. 17ECh. 4.4 - Prob. 18ECh. 4.4 - Prob. 19ECh. 4.4 - Prob. 20ECh. 4.4 - Prob. 21ECh. 4.4 - Prob. 22ECh. 4.4 - Prob. 23ECh. 4.4 - Prob. 24ECh. 4.4 - Solve each exponential apiarian in Exercises...Ch. 4.4 - Prob. 26ECh. 4.4 - Prob. 27ECh. 4.4 - Prob. 28ECh. 4.4 - Solve each exponential equation in Exercises...Ch. 4.4 - Prob. 30ECh. 4.4 - Prob. 31ECh. 4.4 - Prob. 32ECh. 4.4 - Solve each exponential equation in Exercises...Ch. 4.4 - Prob. 34ECh. 4.4 - Prob. 35ECh. 4.4 - Prob. 36ECh. 4.4 - Solve each exponential equation in Exercises...Ch. 4.4 - Prob. 38ECh. 4.4 - Solve each exponential equation in Exercises 2348....Ch. 4.4 - Prob. 40ECh. 4.4 - Solve each exponential equation in Exercises 2348....Ch. 4.4 - Prob. 42ECh. 4.4 - Prob. 43ECh. 4.4 - Prob. 44ECh. 4.4 - Solve each exponential equation in Exercises 2348....Ch. 4.4 - Prob. 46ECh. 4.4 - Prob. 47ECh. 4.4 - Solve each exponential equation in Exercises...Ch. 4.4 - Solve each logarithmic equation in Exercises...Ch. 4.4 - Prob. 50ECh. 4.4 - Solve each logarithmic equation in Exercises...Ch. 4.4 - Prob. 52ECh. 4.4 - Solve each logarithmic equation in Exercises...Ch. 4.4 - Prob. 54ECh. 4.4 - Solve each logarithmic equation in Exercises...Ch. 4.4 - Solve each logarithmic equation in Exercises...Ch. 4.4 - Solve each logarithmic equation in Exercises...Ch. 4.4 - Solve each logarithmic equation in Exercises...Ch. 4.4 - Solve each logarithmic equation in Exercises...Ch. 4.4 - Solve each logarithmic equation in Exercises...Ch. 4.4 - Solve each logarithmic equation in Exercises...Ch. 4.4 - Prob. 62ECh. 4.4 - Solve each logarithmic equation in Exercises...Ch. 4.4 - Prob. 64ECh. 4.4 - Solve each logarithmic equation in Exercises...Ch. 4.4 - Prob. 66ECh. 4.4 - Solve each logarithmic equation in Exercises...Ch. 4.4 - Prob. 68ECh. 4.4 - Solve each logarithmic equation in Exercises...Ch. 4.4 - Prob. 70ECh. 4.4 - Solve each logarithmic equation in Exercises...Ch. 4.4 - Solve each logarithmic equation in Exercises...Ch. 4.4 - Solve each logarithmic equation in Exercises...Ch. 4.4 - Prob. 74ECh. 4.4 - Solve each logarithmic equation in Exercises...Ch. 4.4 - Prob. 76ECh. 4.4 - Solve each logarithmic equation in Exercises...Ch. 4.4 - Prob. 78ECh. 4.4 - Solve each logarithmic equation in Exercises...Ch. 4.4 - Prob. 80ECh. 4.4 - Solve each logarithmic equation in Exercises...Ch. 4.4 - Prob. 82ECh. 4.4 - Solve each logarithmic equation in Exercises...Ch. 4.4 - Prob. 84ECh. 4.4 - Solve each logarithmic equation in Exercises...Ch. 4.4 - Prob. 86ECh. 4.4 - Solve each logarithmic equation in Exercises...Ch. 4.4 - Prob. 88ECh. 4.4 - Solve each logarithmic equation in Exercises...Ch. 4.4 - Prob. 90ECh. 4.4 - Solve each logarithmic equation in Exercises...Ch. 4.4 - Solve each logarithmic equation in Exercises...Ch. 4.4 - In Exercises 93-102, solve each equation.
93.
Ch. 4.4 - Prob. 94ECh. 4.4 - Prob. 95ECh. 4.4 - Prob. 96ECh. 4.4 - Prob. 97ECh. 4.4 - Prob. 98ECh. 4.4 - Prob. 99ECh. 4.4 - In Exercises 93-102, solve each equation.
100.
Ch. 4.4 - Prob. 101ECh. 4.4 - Prob. 102ECh. 4.4 - Prob. 103ECh. 4.4 - 104. The formula models the population of Texas....Ch. 4.4 - The function models the percentage of surface...Ch. 4.4 - Prob. 106ECh. 4.4 - Prob. 107ECh. 4.4 - Prob. 108ECh. 4.4 - Prob. 109ECh. 4.4 - Prob. 110ECh. 4.4 - Prob. 111ECh. 4.4 - Prob. 112ECh. 4.4 - Prob. 113ECh. 4.4 - Prob. 114ECh. 4.4 - Prob. 115ECh. 4.4 - Prob. 116ECh. 4.4 - Prob. 117ECh. 4.4 - Prob. 118ECh. 4.4 - The pH scale is used to measure the acidity or...Ch. 4.4 - The pH scale is used to measure the acidity or...Ch. 4.4 - Prob. 121ECh. 4.4 - Prob. 122ECh. 4.4 - Prob. 123ECh. 4.4 - Prob. 124ECh. 4.4 - Prob. 125ECh. 4.4 - Prob. 126ECh. 4.4 - Prob. 127ECh. 4.4 - Prob. 128ECh. 4.4 - Prob. 129ECh. 4.4 - Prob. 130ECh. 4.4 - Prob. 131ECh. 4.4 - Prob. 132ECh. 4.4 - Prob. 133ECh. 4.4 - Prob. 134ECh. 4.4 - Prob. 135ECh. 4.4 - 136. The function models the weight, W (t). in...Ch. 4.4 - Prob. 137ECh. 4.4 - Prob. 138ECh. 4.4 - Prob. 139ECh. 4.4 - Prob. 140ECh. 4.4 - Prob. 141ECh. 4.4 - Prob. 142ECh. 4.4 - Prob. 143ECh. 4.4 - In Exercises 141-144, determine whether each...Ch. 4.4 - Prob. 145ECh. 4.4 - Prob. 146ECh. 4.4 - Prob. 147ECh. 4.4 - Prob. 148ECh. 4.4 - Prob. 149ECh. 4.4 - Prob. 150ECh. 4.4 - Prob. 151ECh. 4.4 - Prob. 152ECh. 4.4 - Prob. 153ECh. 4.4 - Prob. 154ECh. 4.4 - Prob. 155ECh. 4.5 - Fill in each blank so that the resulting statement...Ch. 4.5 - Fill in each blank so that the resulting statement...Ch. 4.5 - Prob. 3CVCCh. 4.5 - Prob. 4CVCCh. 4.5 - Prob. 5CVCCh. 4.5 - Prob. 6CVCCh. 4.5 - Prob. 7CVCCh. 4.5 - Prob. 1ECh. 4.5 - Prob. 2ECh. 4.5 - Prob. 3ECh. 4.5 - The exponential models describe the population of...Ch. 4.5 - The exponential models describe the population of...Ch. 4.5 - The exponential models describe the population of...Ch. 4.5 - About the size of New Jersey, Israel has seen its...Ch. 4.5 - Prob. 8ECh. 4.5 - In Exercises 9-14, complete the table. Round...Ch. 4.5 - Prob. 10ECh. 4.5 - Prob. 11ECh. 4.5 - In Exercises 9-14, complete the table. Round...Ch. 4.5 - Prob. 13ECh. 4.5 - In Exercises 9-14, complete the table. Round...Ch. 4.5 - An artifact originally had 16 grams of carbon-14...Ch. 4.5 - Prob. 16ECh. 4.5 - Prob. 17ECh. 4.5 - Prob. 18ECh. 4.5 - Use the exponential decay model for carbon-14,...Ch. 4.5 - Use the exponential decay model for carbon-14, ,...Ch. 4.5 - Prob. 21ECh. 4.5 - Prob. 22ECh. 4.5 - Prob. 23ECh. 4.5 - Prob. 24ECh. 4.5 - Prob. 25ECh. 4.5 - Prob. 26ECh. 4.5 - Prob. 27ECh. 4.5 - Prob. 28ECh. 4.5 - Use the exponential decay model, A=A0ekt to solve...Ch. 4.5 - Prob. 30ECh. 4.5 - Prob. 31ECh. 4.5 - Prob. 32ECh. 4.5 - Prob. 33ECh. 4.5 - Prob. 34ECh. 4.5 - Prob. 35ECh. 4.5 - Prob. 36ECh. 4.5 - 37. The logistic growth function
describes the...Ch. 4.5 - We see from the calculator screen at the bottom of...Ch. 4.5 - Shown, again, in the following table is world...Ch. 4.5 - Prob. 40ECh. 4.5 - Prob. 41ECh. 4.5 - Shown, again, in the following table is world...Ch. 4.5 - Prob. 43ECh. 4.5 - Prob. 44ECh. 4.5 - The logistic growth function P(x)=901+271e0.122x...Ch. 4.5 - Prob. 46ECh. 4.5 - Prob. 47ECh. 4.5 - Exercises 47-51 present data in the form of...Ch. 4.5 - Prob. 49ECh. 4.5 - Prob. 50ECh. 4.5 - Prob. 51ECh. 4.5 - Exercises 47-52 present data in the form of...Ch. 4.5 - Prob. 53ECh. 4.5 - Prob. 54ECh. 4.5 - Prob. 55ECh. 4.5 - Prob. 56ECh. 4.5 - Prob. 57ECh. 4.5 - 58. How can you tell whether an exponential model...Ch. 4.5 - Prob. 59ECh. 4.5 - Prob. 60ECh. 4.5 - Prob. 61ECh. 4.5 - 62. Describe the shape of a scatter plot that...Ch. 4.5 - Prob. 63ECh. 4.5 - Prob. 64ECh. 4.5 - Prob. 65ECh. 4.5 - In Example 1 on page 520, we used two data paints...Ch. 4.5 - Prob. 67ECh. 4.5 - Prob. 68ECh. 4.5 - Prob. 69ECh. 4.5 - Prob. 70ECh. 4.5 - The figure shows the number of people in the...Ch. 4.5 - In Exercises 47-52, you determined the best choice...Ch. 4.5 - Prob. 73ECh. 4.5 - Make Sense? In Exercises 73-76, determine whether...Ch. 4.5 - Make Sense? In Exercises 73-76, determine whether...Ch. 4.5 - Prob. 76ECh. 4.5 - Prob. 77ECh. 4.5 - Prob. 78ECh. 4.5 - The exponential growth models describe the...Ch. 4.5 - Prob. 80ECh. 4.5 - Prob. 81ECh. 4.5 - Prob. 82ECh. 4.5 - Prob. 83ECh. 4.5 - Prob. 84ECh. 4.5 - Prob. 85ECh. 4.5 - Prob. 86ECh. 4.5 - Prob. 87ECh. 4.5 - Prob. 88ECh. 4 - In Exercises 1-5, graph f and g in the same...Ch. 4 - In Exercises 1-5, graph f and g in the same...Ch. 4 - In Exercises 1-5, graph f and g in the same...Ch. 4 - In Exercises 1-5, graph f and g in the same...Ch. 4 - In Exercises 1-5, graph f and g in the same...Ch. 4 - Prob. 6MCCPCh. 4 - In Exercises 6-9, find the domain of each...Ch. 4 - In Exercises 6-9, find the domain of each function...Ch. 4 - In Exercises 6-9, find the domain of each...Ch. 4 - In Exercises 10-20, evaluate each expression...Ch. 4 - Prob. 11MCCPCh. 4 - In Exercises 10-20, evaluate each expression...Ch. 4 - Prob. 13MCCPCh. 4 - Prob. 14MCCPCh. 4 - In Exercises 10-20, evaluate each expression...Ch. 4 - In Exercises 10-20, evaluate each expression...Ch. 4 - In Exercises 10-20, evaluate each expression...Ch. 4 - Prob. 18MCCPCh. 4 - Prob. 19MCCPCh. 4 - Prob. 20MCCPCh. 4 - Prob. 21MCCPCh. 4 - Prob. 22MCCPCh. 4 - Prob. 23MCCPCh. 4 - Prob. 24MCCPCh. 4 - Prob. 25MCCPCh. 4 - Prob. 26MCCPCh. 4 - In Exercises 1-4, the graph of an exponential...Ch. 4 - Prob. 2RECh. 4 - Prob. 3RECh. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - In Exercises 5-9, graph f and g in the same...Ch. 4 - In Exercises 5–9, graph f and g in the same...Ch. 4 - In Exercises 5-9, graph f and g in the same...Ch. 4 - In Exercises 5-9, graph f and g in the same...Ch. 4 - Use the compound interest formulas to solve...Ch. 4 - 11. Suppose that you have $14,000 to invest. Which...Ch. 4 - 12. A cup of coffee is taken out of a microwave...Ch. 4 - 13.
Ch. 4 - 3=log4xCh. 4 - log318=yCh. 4 - In Exercises 16-18, write each equation in its...Ch. 4 - In Exercises 16-18, write each equation in its...Ch. 4 - In Exercises 16-18, write each equation in its...Ch. 4 - In Exercises 19-29, evaluate each expression...Ch. 4 - In Exercises 19-29, evaluate each expression...Ch. 4 - In Exercises 19-29, evaluate each expression...Ch. 4 - In Exercises 19-29, evaluate each expression...Ch. 4 - In Exercises 19-29, evaluate each expression...Ch. 4 - In Exercises 19-29, evaluate each expression...Ch. 4 - In Exercises 19-29, evaluate each expression...Ch. 4 - In Exercises 19-29, evaluate each expression...Ch. 4 - In Exercises 19-29, evaluate each expression...Ch. 4 - In Exercises 19-29, evaluate each expression...Ch. 4 - In Exercises 19-29, evaluate each expression...Ch. 4 - Graph f(x)=2x and g(x)=log2x in the same...Ch. 4 - Prob. 31RECh. 4 - Prob. 32RECh. 4 - Prob. 33RECh. 4 - Prob. 34RECh. 4 - Prob. 35RECh. 4 - Prob. 36RECh. 4 - Prob. 37RECh. 4 - Prob. 38RECh. 4 - Prob. 39RECh. 4 - Prob. 40RECh. 4 - In Exercises 41-43, find the domain of each...Ch. 4 - In Exercises 41-43, find the domain of each...Ch. 4 - In Exercises 41-43, find the domain of each...Ch. 4 - In Exercises 44-46, use inverse properties of...Ch. 4 - In Exercises 44-46, use inverse properties of...Ch. 4 - In Exercises 44-46, use inverse properties of...Ch. 4 - 47. On the Richter scale, the magnitude, R, of an...Ch. 4 - 48. Students in a psychology class look a final...Ch. 4 - 49. The formula
describes the lime, t, in weeks,...Ch. 4 - In Exercises 50-53, use properties of logarithms...Ch. 4 - In Exercises 50-53, use properties of logarithms...Ch. 4 - Prob. 52RECh. 4 - Prob. 53RECh. 4 - In Exercises 54-57, use properties of logarithms...Ch. 4 - Prob. 55RECh. 4 - Prob. 56RECh. 4 - Prob. 57RECh. 4 - In Exercises 58-59, use common logarithms or...Ch. 4 - Prob. 59RECh. 4 - Prob. 60RECh. 4 - Prob. 61RECh. 4 - Prob. 62RECh. 4 - Prob. 63RECh. 4 - Prob. 64RECh. 4 - Prob. 65RECh. 4 - Prob. 66RECh. 4 - Prob. 67RECh. 4 - Prob. 68RECh. 4 - Prob. 69RECh. 4 - In Exercises 64-73, solve each exponential...Ch. 4 - Prob. 71RECh. 4 - Prob. 72RECh. 4 - Prob. 73RECh. 4 - Prob. 74RECh. 4 - Prob. 75RECh. 4 - Prob. 76RECh. 4 - Prob. 77RECh. 4 - Prob. 78RECh. 4 - Prob. 79RECh. 4 - Prob. 80RECh. 4 - 81. Newest Dinosaur: The PC-o5aurus? For the...Ch. 4 - 82. Years after “Brown v. Board" In 1954, the...Ch. 4 - 83. Use the formula for compound interest with n...Ch. 4 - Prob. 84RECh. 4 - Prob. 85RECh. 4 - 86. According to the U.S. Bureau of I he Census,...Ch. 4 - Prob. 87RECh. 4 - Prob. 88RECh. 4 - Prob. 89RECh. 4 - Exercises 89-91 present data in the form of...Ch. 4 - Exercises 89-91 present data in the form of...Ch. 4 - Prob. 92RECh. 4 - Prob. 93RECh. 4 - Prob. 94RECh. 4 - Graph f(x)=2x and g(x)=2x+1 in the same...Ch. 4 - Prob. 2TCh. 4 - Prob. 3TCh. 4 - Prob. 4TCh. 4 - Prob. 5TCh. 4 - In Exercises 6-7, use properties of logarithms to...Ch. 4 - Prob. 7TCh. 4 - Prob. 8TCh. 4 - Prob. 9TCh. 4 - Prob. 10TCh. 4 - Prob. 11TCh. 4 - Prob. 12TCh. 4 - Prob. 13TCh. 4 - Prob. 14TCh. 4 - Prob. 15TCh. 4 - Prob. 16TCh. 4 - Prob. 17TCh. 4 - Prob. 18TCh. 4 - Prob. 19TCh. 4 - Prob. 20TCh. 4 - Prob. 21TCh. 4 - Prob. 22TCh. 4 - Prob. 23TCh. 4 - Prob. 24TCh. 4 - Prob. 25TCh. 4 - Prob. 26TCh. 4 - The 2010 population of Asia was 4121 million; in...Ch. 4 - Use the exponential decay model, A=A0eLt, to solve...Ch. 4 - Prob. 29TCh. 4 - Prob. 30TCh. 4 - Prob. 31TCh. 4 - Prob. 32TCh. 4 - Prob. 33TCh. 4 - 34. Rewrite in terms of base e. Express the answer...Ch. 4 - In Exercises 1-8, solve each equation or...Ch. 4 - In Exercises 1-8, solve each equation or...Ch. 4 - Prob. 3CRECh. 4 - Prob. 4CRECh. 4 - Prob. 5CRECh. 4 - Prob. 6CRECh. 4 - Prob. 7CRECh. 4 - Prob. 8CRECh. 4 - Prob. 9CRECh. 4 - Prob. 10CRECh. 4 - Prob. 11CRECh. 4 - Prob. 12CRECh. 4 - Prob. 13CRECh. 4 - Prob. 14CRECh. 4 - Prob. 15CRECh. 4 - Prob. 16CRECh. 4 - Prob. 17CRECh. 4 - Prob. 18CRECh. 4 - Prob. 19CRECh. 4 - Prob. 20CRE
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Similar questions
- A utility pole is 35 ft tall. The pole creates a 50 ft shadow. What is the angle of elevation of the sun? Round your answer to the nearest degree. Show your work. nswer:arrow_forwardWrite the expression as a simplified rational expression. Show your work. 1 6 + 5 1 x + 1arrow_forwardThe population of a town was 5655 in 2010. The population grows at a rate of 1.4% annually. (a) Use the exponential growth model to write an equation that estimates the population t years after 2010. (a) Estimate the population of the town in 2022. Show your work.arrow_forward
- Simplify the expression (x³ - 5x² + 7x - 12) ÷ (x − 4) using long division. Show your work.arrow_forwardx² + 3x - 28 Simplify the expression x² - 7x+12. Show nswer: your work.arrow_forwardA savings account is started with an initial deposit of $500. The account earns 1.5% interest compounded annually. (a) Write an equation to represent the amount of money in the account as a function of time in years. (b) Find the amount of time it takes for the account balance to reach $800. Show your work.arrow_forward
- (a) Use the fundamental theorem of algebra to determine the number of roots for 2x² +4x+7. (b) What are the roots of 2x² +4x+7? Show your work.arrow_forwardConsider the function f(x)=x³ + 2x² − 3 (a) Graph the function. (b) What are the x- and y-intercepts of the graph?arrow_forwardLet 2 A = 4 3 -4 0 1 (a) Show that v = eigenvalue. () is an eigenvector of A and find the corresponding (b) Find the characteristic polynomial of A and factorise it. Hint: the answer to (a) may be useful. (c) Determine all eigenvalues of A and find bases for the corresponding eigenspaces. (d) Find an invertible matrix P and a diagonal matrix D such that P-¹AP = D.arrow_forward
- (c) Let 6 0 0 A = -10 4 8 5 1 2 (i) Find the characteristic polynomial of A and factorise it. (ii) Determine all eigenvalues of A and find bases for the corresponding eigenspaces. (iii) Is A diagonalisable? Give reasons for your answer.arrow_forwardmost 2, and let Let P2 denote the vector space of polynomials of degree at D: P2➡ P2 be the transformation that sends a polynomial p(t) = at² + bt+c in P2 to its derivative p'(t) 2at+b, that is, D(p) = p'. (a) Prove that D is a linear transformation. (b) Find a basis for the kernel ker(D) of the linear transformation D and compute its nullity. (c) Find a basis for the image im(D) of the linear transformation D and compute its rank. (d) Verify that the Rank-Nullity Theorem holds for the linear transformation D. (e) Find the matrix representation of D in the standard basis (1,t, t2) of P2.arrow_forward(c) Let A = -1 3 -4 12 3 3 -9 (i) Find bases for row(A), col(A) and N(A). (ii) Determine the rank and nullity of A, and verify that the Rank-Nullity Theorem holds for the above matrix A.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Asymptotes - What are they? : ExamSolutions Maths Revision; Author: ExamSolutions;https://www.youtube.com/watch?v=5Hl_WJXcR6M;License: Standard YouTube License, CC-BY