College Algebra
1st Edition
ISBN: 9780078035630
Author: Julie Miller
Publisher: MCGRAW-HILL HIGHER EDUCATION
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 4.4, Problem 112PE
!
To determine
To graph: The function
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Math 116 Section 6.4
Example 2: Sketch a graph of f(x) = log₂ (x) + 2 alongside the parent function
-10 -8 -6-4-2
10
8
6
4
2
N
-2
-4
-6
-8
-10
2
4
6 8 10
IV. Evaluation
Construct the table and draw the graph of the functions
y = (2/5)* and y = loga/s) ×
Exercises 77-78: Critical Thinking Complete the follow-
ing for the given graph of an exponential function f.
(a) Give the domain and range of f.
(b) Identify intervals where f is greater than 1 and where
is f less than 1.
(c) Estimate the average rate of change from x = 0 to x = 2.
(d) Identify intervals where f is increasing and where f is
decreasing.
(e) Give any intercepts.
(f) If x is positive and doubles, what happens to f(x)?
77.
78.
-3
I
32
-3
(y=f(x)
3
فيا
-2-
-3-11-
3
표
y = f(x)
3
Chapter 4 Solutions
College Algebra
Ch. 4.1 - Prob. 1SPCh. 4.1 - Skill Practice
2. Use the horizontal line test to...Ch. 4.1 - Prob. 3SPCh. 4.1 - Prob. 4SPCh. 4.1 - Skill Practice
5. Write an equation for the...Ch. 4.1 - Prob. 6SPCh. 4.1 - Prob. 7SPCh. 4.1 - Prob. 8SPCh. 4.1 - Concept Connections Given the function...Ch. 4.1 - Prob. 2PE
Ch. 4.1 - 2. The graph of a function and its inverse are...Ch. 4.1 - Prob. 4PECh. 4.1 - A function defined by y=f(x) (is/is not) a...Ch. 4.1 - Prob. 6PECh. 4.1 - 5. Let f be one-to-one function and let g be the...Ch. 4.1 - The notation ________ is often used to represent...Ch. 4.1 - Prob. 9PECh. 4.1 - Prob. 10PECh. 4.1 - Objective 1: Identify One-to-One Functions For...Ch. 4.1 - Prob. 12PECh. 4.1 - Objective 1: Identify One-to-One Functions
For...Ch. 4.1 - Objective 1: Identify One-to-One Functions
For...Ch. 4.1 - Prob. 15PECh. 4.1 - Prob. 16PECh. 4.1 - Objective 1: Identify One-to-One Functions For...Ch. 4.1 - Objective 1: Identify One-to-One Functions For...Ch. 4.1 - For Exercises 1322, determine if the relation...Ch. 4.1 - For Exercises 1322, determine if the relation...Ch. 4.1 - For Exercises 1322, determine if the relation...Ch. 4.1 - For Exercises 1322, determine if the relation...Ch. 4.1 - For Exercises 1322, determine if the relation...Ch. 4.1 - For Exercises 13–22, determine if the relation...Ch. 4.1 - For Exercises 1322, determine if the relation...Ch. 4.1 - For Exercises 13–22, determine if the relation...Ch. 4.1 - For Exercises 1322, determine if the relation...Ch. 4.1 - For Exercises 13–22, determine if the relation...Ch. 4.1 - For Exercises 23–30, use the definition of ...Ch. 4.1 - For Exercises 2330, use the definition of...Ch. 4.1 - For Exercises 2330, use the definition of...Ch. 4.1 - For Exercises 2330, use the definition of...Ch. 4.1 - For Exercises 23–30, use the definition of ...Ch. 4.1 - For Exercises 23–30, use the definition of ...Ch. 4.1 - For Exercises 2330, use the definition of...Ch. 4.1 - For Exercises 23–30, use the definition of ...Ch. 4.1 - Objective 2: Determine Whether Two Functions Are...Ch. 4.1 - Objective 2: Determine Whether Two Functions Are...Ch. 4.1 - Objective 2: Determine Whether Two Functions Are...Ch. 4.1 - Objective 2: Determine Whether Two Functions Are...Ch. 4.1 - Objective 2: Determine Whether Two Functions Are...Ch. 4.1 - Prob. 42PECh. 4.1 - 37. There were 2000 applicants for enrollment to...Ch. 4.1 - 38. The monthly sales for January for a whole...Ch. 4.1 - Objective 3: Find the Inverse of a Function a....Ch. 4.1 - a. Show that f(x)=4x+4 defines a one-to-one...Ch. 4.1 - For Exercises 41–52, a one-to-one function is...Ch. 4.1 - For Exercises 41–52, a one-to-one function is...Ch. 4.1 - For Exercises 4152, a one-to-one function is...Ch. 4.1 - For Exercises 4152, a one-to-one function is...Ch. 4.1 - For Exercises 4152, a one-to-one function is...Ch. 4.1 - For Exercises 4152, a one-to-one function is...Ch. 4.1 - For Exercises 41–52, a one-to-one function is...Ch. 4.1 - For Exercises 4152, a one-to-one function is...Ch. 4.1 - For Exercises 41–52, a one-to-one function is...Ch. 4.1 - Prob. 56PECh. 4.1 - For Exercises 41–52, a one-to-one function is...Ch. 4.1 - For Exercises 41–52, a one-to-one function is...Ch. 4.1 - a. Graph f(x)=x23;x0. (See Example 7) b. From the...Ch. 4.1 - Prob. 60PECh. 4.1 - a. Graph f(x)=x+1. (See Example 8) b. From the...Ch. 4.1 - a. Graph f(x)=x2. b. From the graph of f, is f a...Ch. 4.1 - Prob. 63PECh. 4.1 - Given that the domain of a one-to-one function f...Ch. 4.1 - Prob. 65PECh. 4.1 - Prob. 66PECh. 4.1 - Prob. 67PECh. 4.1 - Prob. 68PECh. 4.1 - Prob. 69PECh. 4.1 - Prob. 70PECh. 4.1 - Prob. 71PECh. 4.1 - For Exercises 61–66, fill in the blanks and...Ch. 4.1 - For Exercises 6770, find the inverse mentally....Ch. 4.1 - Prob. 74PECh. 4.1 - Prob. 75PECh. 4.1 - Prob. 76PECh. 4.1 - Mixed Exercises
For Exercises 71–74, the graph of...Ch. 4.1 - Prob. 78PECh. 4.1 - Mixed Exercises
For Exercises 71–74, the graph of...Ch. 4.1 - Prob. 80PECh. 4.1 - Prob. 81PECh. 4.1 - Prob. 82PECh. 4.1 - Prob. 83PECh. 4.1 - Prob. 84PECh. 4.1 - Prob. 85PECh. 4.1 - For Exercises 77–80, determine if the statement is...Ch. 4.1 - Prob. 87PECh. 4.1 - 84. At a cruising altitude of 35,000 ft, a certain...Ch. 4.1 - The millage rate is the amount of property tax per...Ch. 4.1 - Prob. 90PECh. 4.1 - Prob. 91PECh. 4.1 - Prob. 92PECh. 4.1 - Prob. 93PECh. 4.1 - Prob. 94PECh. 4.1 - Prob. 95PECh. 4.1 - 90. Explain why the domain of must be restricted...Ch. 4.1 - Prob. 97PECh. 4.1 - Prob. 98PECh. 4.1 - Show that every increasing function is one-to-one.Ch. 4.1 - 94. A function is said to be periodic if there...Ch. 4.1 - Prob. 101PECh. 4.2 - Skill Practice
1. Graph the functions.
a.
b.
Ch. 4.2 - Prob. 2SPCh. 4.2 - Skill Practice Explain how the graph of f(x)=ex1...Ch. 4.2 - Prob. 4SPCh. 4.2 - Skill Practice Cesium-137 is a radioactive metal...Ch. 4.2 - Prob. 1PECh. 4.2 - Prob. 2PECh. 4.2 - Prob. 3PECh. 4.2 - Prob. 4PECh. 4.2 - Prob. 5PECh. 4.2 - Prob. 6PECh. 4.2 - Prob. 7PECh. 4.2 - Prob. 8PECh. 4.2 - Prob. 9PECh. 4.2 - The graph of f(x)=(35)x is (increasing/decreasing)...Ch. 4.2 - Prob. 11PECh. 4.2 - Prob. 12PECh. 4.2 - All exponential functions f(x)=bx pass through the...Ch. 4.2 - Prob. 14PECh. 4.2 - Prob. 15PECh. 4.2 - Prob. 16PECh. 4.2 - Prob. 17PECh. 4.2 - Prob. 18PECh. 4.2 - Objective 1: Graph Exponential Functions For...Ch. 4.2 - Objective 1: Graph Exponential Functions For...Ch. 4.2 - Objective 1: Graph Exponential Functions
For...Ch. 4.2 - Objective 1: Graph Exponential Functions
For...Ch. 4.2 - 13. Which functions are exponential...Ch. 4.2 - 14. Which functions are exponential functions?...Ch. 4.2 - For Exercises 15–22, graph the functions and write...Ch. 4.2 - For Exercises 1522, graph the functions and write...Ch. 4.2 - For Exercises 1522, graph the functions and write...Ch. 4.2 - For Exercises 1522, graph the functions and write...Ch. 4.2 - For Exercises 1522, graph the functions and write...Ch. 4.2 - For Exercises 15–22, graph the functions and write...Ch. 4.2 - For Exercises 15–22, graph the functions and write...Ch. 4.2 - For Exercises 15–22, graph the functions and write...Ch. 4.2 - For Exercises 2332, a. Use transformations of the...Ch. 4.2 - For Exercises 2332, a. Use transformations of the...Ch. 4.2 - For Exercises 2332, a. Use transformations of the...Ch. 4.2 - For Exercises 23–32,
a. Use transformations of...Ch. 4.2 - For Exercises 23–32,
a. Use transformations of...Ch. 4.2 - For Exercises 23–32,
a. Use transformations of...Ch. 4.2 - For Exercises 23–32,
a. Use transformations of...Ch. 4.2 - For Exercises 2332, a. Use transformations of the...Ch. 4.2 - For Exercises 23–32,
a. Use transformations of...Ch. 4.2 - For Exercises 2332, a. Use transformations of the...Ch. 4.2 - For Exercises 33–36,
a. Use transformations of...Ch. 4.2 - Prob. 44PECh. 4.2 - For Exercises 33–36,
a. Use transformations of...Ch. 4.2 - Prob. 46PECh. 4.2 - Objective 2: Evaluate the Exponential Function...Ch. 4.2 - Prob. 48PECh. 4.2 - For Exercises 39–44,
a. Use transformations of...Ch. 4.2 - For Exercises 39–44,
a. Use transformations of...Ch. 4.2 - For Exercises 3944, a. Use transformations of the...Ch. 4.2 - For Exercises 39–44,
a. Use transformations of...Ch. 4.2 - For Exercises 3944, a. Use transformations of the...Ch. 4.2 - For Exercises 39–44,
a. Use transformations of...Ch. 4.2 - Objective 3: Use Exponential Functions to Compute...Ch. 4.2 - Objective 3: Use Exponential Functions to Compute...Ch. 4.2 - For Exercises 47–48, suppose that P dollars in...Ch. 4.2 - For Exercises 4748, suppose that P dollars in...Ch. 4.2 - Bethany needs to borrow $10,000. She can borrow...Ch. 4.2 - 50. Al needs to borrow $15,000 to buy a car. He...Ch. 4.2 - Jerome wants to invest $25,000 as part of his...Ch. 4.2 - 52. Heather wants to invest $35,000 of her...Ch. 4.2 - Strontium-90 (90Sr) is a by-product of nuclear...Ch. 4.2 - 54. In 2006, the murder of Alexander Litvinenko, a...Ch. 4.2 - Prob. 65PECh. 4.2 - The population of Canada in 2010 was approximately...Ch. 4.2 - Prob. 67PECh. 4.2 - Prob. 68PECh. 4.2 - Newtons law of cooling indicates that the...Ch. 4.2 - Prob. 70PECh. 4.2 - Prob. 71PECh. 4.2 - Prob. 72PECh. 4.2 - Prob. 73PECh. 4.2 - Prob. 74PECh. 4.2 - Prob. 75PECh. 4.2 - Prob. 76PECh. 4.2 - Prob. 77PECh. 4.2 - Prob. 78PECh. 4.2 - Prob. 79PECh. 4.2 - Prob. 80PECh. 4.2 - Prob. 81PECh. 4.2 - Prob. 82PECh. 4.2 - Prob. 83PECh. 4.2 - Prob. 84PECh. 4.2 - Prob. 85PECh. 4.2 - Prob. 86PECh. 4.2 - Prob. 87PECh. 4.2 - Prob. 88PECh. 4.2 - Prob. 89PECh. 4.2 - Prob. 90PECh. 4.2 - Prob. 91PECh. 4.2 - Prob. 92PECh. 4.2 - Prob. 93PECh. 4.2 - Prob. 94PECh. 4.2 - Prob. 95PECh. 4.2 - Prob. 96PECh. 4.2 - Prob. 97PECh. 4.3 - Skill Practice
1. Write each equation in...Ch. 4.3 - Prob. 2SPCh. 4.3 - Prob. 3SPCh. 4.3 - Prob. 4SPCh. 4.3 - Prob. 5SPCh. 4.3 - Prob. 6SPCh. 4.3 - Prob. 7SPCh. 4.3 - Prob. 8SPCh. 4.3 - Prob. 9SPCh. 4.3 - Prob. 10SPCh. 4.3 - Prob. 1PECh. 4.3 - Prob. 2PECh. 4.3 - Prob. 3PECh. 4.3 - Prob. 4PECh. 4.3 - Prob. 5PECh. 4.3 - Prob. 6PECh. 4.3 - Prob. 7PECh. 4.3 - Prob. 8PECh. 4.3 - Prob. 9PECh. 4.3 - Prob. 10PECh. 4.3 - Prob. 11PECh. 4.3 - 4. Given the base is understood to be __________...Ch. 4.3 - Prob. 13PECh. 4.3 - Prob. 14PECh. 4.3 - Prob. 15PECh. 4.3 - Prob. 16PECh. 4.3 - Prob. 17PECh. 4.3 - Prob. 18PECh. 4.3 - For the exercises in this set, assume that all...Ch. 4.3 - For the exercises in this set, assume that all...Ch. 4.3 - For the exercises in this set, assume that all...Ch. 4.3 - For the exercises in this set, assume that all...Ch. 4.3 - For the exercises in this set, assume that all...Ch. 4.3 - For the exercises in this set, assume that all...Ch. 4.3 - For the exercises in this set, assume that all...Ch. 4.3 - For the exercises in this set, assume that all...Ch. 4.3 - For Exercises 17–24, write the equation in...Ch. 4.3 - For Exercises 17–24, write the equation in...Ch. 4.3 - For Exercises 17–24, write the equation in...Ch. 4.3 - For Exercises 1724, write the equation in...Ch. 4.3 - For Exercises 17–24, write the equation in...Ch. 4.3 - For Exercises 1724, write the equation in...Ch. 4.3 - For Exercises 1724, write the equation in...Ch. 4.3 - For Exercises 17–24, write the equation in...Ch. 4.3 - Objective 2: Evaluate Logarithmic Expressions
For...Ch. 4.3 - Objective 2: Evaluate Logarithmic Expressions
For...Ch. 4.3 - Objective 2: Evaluate Logarithmic Expressions For...Ch. 4.3 - Objective 2: Evaluate Logarithmic Expressions For...Ch. 4.3 - Objective 2: Evaluate Logarithmic Expressions For...Ch. 4.3 - Objective 2: Evaluate Logarithmic Expressions For...Ch. 4.3 - Objective 2: Evaluate Logarithmic Expressions
For...Ch. 4.3 - Objective 2: Evaluate Logarithmic Expressions For...Ch. 4.3 - Objective 2: Evaluate Logarithmic Expressions For...Ch. 4.3 - Objective 2: Evaluate Logarithmic Expressions For...Ch. 4.3 - Objective 2: Evaluate Logarithmic Expressions For...Ch. 4.3 - Objective 2: Evaluate Logarithmic Expressions For...Ch. 4.3 - Objective 2: Evaluate Logarithmic Expressions
For...Ch. 4.3 - Objective 2: Evaluate Logarithmic Expressions For...Ch. 4.3 - Objective 2: Evaluate Logarithmic Expressions For...Ch. 4.3 - Objective 2: Evaluate Logarithmic Expressions
For...Ch. 4.3 - Objective 2: Evaluate Logarithmic Expressions For...Ch. 4.3 - Objective 2: Evaluate Logarithmic Expressions
For...Ch. 4.3 - Objective 2: Evaluate Logarithmic Expressions For...Ch. 4.3 - Objective 2: Evaluate Logarithmic Expressions For...Ch. 4.3 - Prob. 55PECh. 4.3 - Prob. 56PECh. 4.3 - For Exercises 53–54, approximate for the given...Ch. 4.3 - Prob. 58PECh. 4.3 - Objective 3: Apply Basic Properties of Logarithms...Ch. 4.3 - Prob. 60PECh. 4.3 - Objective 3: Apply Basic Properties of...Ch. 4.3 - Prob. 62PECh. 4.3 - Objective 3: Apply Basic Properties of...Ch. 4.3 - Prob. 64PECh. 4.3 - Objective 3: Apply Basic Properties of Logarithms...Ch. 4.3 - Objective 3: Apply Basic Properties of...Ch. 4.3 - Objective 3: Apply Basic Properties of...Ch. 4.3 - Objective 3: Apply Basic Properties of Logarithms...Ch. 4.3 - Objective 4: Graph Logarithmic Functions
For...Ch. 4.3 - Objective 4: Graph Logarithmic Functions For...Ch. 4.3 - Objective 4: Graph Logarithmic Functions
For...Ch. 4.3 - Objective 4: Graph Logarithmic Functions
For...Ch. 4.3 - Objective 4: Graph Logarithmic Functions
For...Ch. 4.3 - Objective 4: Graph Logarithmic Functions For...Ch. 4.3 - For Exercises 71–78, (See Example 8)
a. Use...Ch. 4.3 - Prob. 76PECh. 4.3 - For Exercises 71–78, (See Example 8)
a. Use...Ch. 4.3 - Prob. 78PECh. 4.3 - For Exercises 71–78, (See Example 8)
a. Use...Ch. 4.3 - Prob. 80PECh. 4.3 - For Exercises 71–78, (See Example 8)
a. Use...Ch. 4.3 - Prob. 82PECh. 4.3 - For Exercises 79–92, write the domain in interval...Ch. 4.3 - Prob. 84PECh. 4.3 - For Exercises 7992, write the domain in interval...Ch. 4.3 - For Exercises 79–92, write the domain in interval...Ch. 4.3 - For Exercises 79–92, write the domain in interval...Ch. 4.3 - For Exercises 79–92, write the domain in interval...Ch. 4.3 - For Exercises 7992, write the domain in interval...Ch. 4.3 - Prob. 90PECh. 4.3 - For Exercises 79–92, write the domain in interval...Ch. 4.3 - Prob. 92PECh. 4.3 - In 1989, the Loma Prieta earthquake damaged the...Ch. 4.3 - Prob. 94PECh. 4.3 - Sounds are produced when vibrating objects create...Ch. 4.3 - Sounds are produced when vibrating objects create...Ch. 4.3 - Scientists use pH scale to represent the level of...Ch. 4.3 - Prob. 98PECh. 4.3 - Scientists categorize sediment size on a base-2...Ch. 4.3 - Prob. 100PECh. 4.3 - Prob. 101PECh. 4.3 - Prob. 102PECh. 4.3 - Prob. 103PECh. 4.3 - Mixed Exercises
For Exercises 99–102,
a. Write...Ch. 4.3 - Prob. 105PECh. 4.3 - Prob. 106PECh. 4.3 - Prob. 107PECh. 4.3 - Prob. 108PECh. 4.3 - Prob. 109PECh. 4.3 - a. Evaluate log33+log327 b. Evaluate log3(327) c....Ch. 4.3 - a. Evaluate log464log44 b. Evaluate log4(644) c....Ch. 4.3 - Prob. 112PECh. 4.3 - Prob. 113PECh. 4.3 - Prob. 114PECh. 4.3 - Prob. 115PECh. 4.3 - 114. The number n of monthly payments of P dollars...Ch. 4.3 - Prob. 117PECh. 4.3 - Prob. 118PECh. 4.3 - Prob. 119PECh. 4.3 - Prob. 120PECh. 4.3 - Prob. 121PECh. 4.3 - Prob. 122PECh. 4.3 - Prob. 123PECh. 4.3 - Prob. 124PECh. 4.3 - Prob. 125PECh. 4.3 - Prob. 126PECh. 4.3 - Prob. 127PECh. 4.3 - Prob. 128PECh. 4.3 - Prob. 129PECh. 4.3 - Prob. 130PECh. 4.3 - Prob. 1PRECh. 4.3 - Prob. 2PRECh. 4.3 - Prob. 3PRECh. 4.3 - Prob. 4PRECh. 4.3 - Prob. 5PRECh. 4.3 - Prob. 6PRECh. 4.3 - Prob. 7PRECh. 4.3 - Prob. 8PRECh. 4.3 - Prob. 9PRECh. 4.3 - For Exercises 1-14,
a. Write the...Ch. 4.3 - Prob. 11PRECh. 4.3 - Prob. 12PRECh. 4.3 - Prob. 13PRECh. 4.3 - Prob. 14PRECh. 4.4 - Skill Practice
1. Write the logarithm as a sum and...Ch. 4.4 - Prob. 2SPCh. 4.4 - Prob. 3SPCh. 4.4 - Prob. 4SPCh. 4.4 - Prob. 5SPCh. 4.4 - Prob. 6SPCh. 4.4 - Prob. 7SPCh. 4.4 - Prob. 8SPCh. 4.4 - Prob. 1PECh. 4.4 - Prob. 2PECh. 4.4 - Prob. 3PECh. 4.4 - Prob. 4PECh. 4.4 - Prob. 5PECh. 4.4 - Prob. 6PECh. 4.4 - Prob. 7PECh. 4.4 - Prob. 8PECh. 4.4 - Prob. 9PECh. 4.4 - Prob. 10PECh. 4.4 - Prob. 11PECh. 4.4 - Prob. 12PECh. 4.4 - Prob. 13PECh. 4.4 - Prob. 14PECh. 4.4 - Prob. 15PECh. 4.4 - Prob. 16PECh. 4.4 - For the exercises in this set, assume that all...Ch. 4.4 - Prob. 18PECh. 4.4 - For the exercises in this set, assume that all...Ch. 4.4 - Prob. 20PECh. 4.4 - For the exercises in this set, assume that all...Ch. 4.4 - Prob. 22PECh. 4.4 - For Exercises 13-18, use the quotient property of...Ch. 4.4 - For Exercises 13-18, use the quotient property of...Ch. 4.4 - For Exercises 13-18, use the quotient property of...Ch. 4.4 - Prob. 26PECh. 4.4 - For Exercises 13-18, use the quotient property of...Ch. 4.4 - Prob. 28PECh. 4.4 - For Exercises 19-24, apply the power property of...Ch. 4.4 - Prob. 30PECh. 4.4 - For Exercises 19-24, apply the power property of...Ch. 4.4 - Prob. 32PECh. 4.4 - For Exercises 19-24, apply the power property of...Ch. 4.4 - Prob. 34PECh. 4.4 - Objective 2: Write a Logarithmic Expression in...Ch. 4.4 - Prob. 36PECh. 4.4 - Prob. 37PECh. 4.4 - Objective 2: Write a Logarithmic Expression in...Ch. 4.4 - Objective 2: Write a Logarithmic Expression in...Ch. 4.4 - Prob. 40PECh. 4.4 - Objective 2: Write a Logarithmic Expression in...Ch. 4.4 - Prob. 42PECh. 4.4 - Objective 2: Write a Logarithmic Expression in...Ch. 4.4 - Prob. 44PECh. 4.4 - Objective 2: Write a Logarithmic Expression in...Ch. 4.4 - Objective 2: Write a Logarithmic Expression in...Ch. 4.4 - Objective 2: Write a Logarithmic Expression in...Ch. 4.4 - Objective 2: Write a Logarithmic Expression in...Ch. 4.4 - Objective 3: Write a Logarithmic Expression as a...Ch. 4.4 - Prob. 50PECh. 4.4 - Objective 3: Write a Logarithmic Expression as a...Ch. 4.4 - Objective 3: Write a Logarithmic Expression as a...Ch. 4.4 - Objective 3: Write a Logarithmic Expression as a...Ch. 4.4 - Prob. 54PECh. 4.4 - Objective 3: Write a Logarithmic Expression as a...Ch. 4.4 - Prob. 56PECh. 4.4 - Objective 3: Write a Logarithmic Expression as a...Ch. 4.4 - Objective 3: Write a Logarithmic Expression as a...Ch. 4.4 - Objective 3: Write a Logarithmic Expression as a...Ch. 4.4 - Prob. 60PECh. 4.4 - Objective 3: Write a Logarithmic Expression as a...Ch. 4.4 - Objective 3: Write a Logarithmic Expression as a...Ch. 4.4 - Objective 3: Write a Logarithmic Expression as a...Ch. 4.4 - Prob. 64PECh. 4.4 - Objective 3: Write a Logarithmic Expression as a...Ch. 4.4 - Objective 3: Write a Logarithmic Expression as a...Ch. 4.4 - Objective 3: Write a Logarithmic Expression as a...Ch. 4.4 - Prob. 68PECh. 4.4 - For Exercises 69-78, use logb20.356,logb30.565,...Ch. 4.4 - Prob. 70PECh. 4.4 - For Exercises 69-78, use logb20.356,logb30.565,...Ch. 4.4 - Prob. 72PECh. 4.4 - For Exercises 69-78, use , and to approximate the...Ch. 4.4 - Prob. 74PECh. 4.4 - For Exercises 69-78, use , and to approximate the...Ch. 4.4 - Prob. 76PECh. 4.4 - For Exercises 69-78, use logb20.356,logb30.565,...Ch. 4.4 - Prob. 78PECh. 4.4 - Objective 4: Apply the Change-of-Base Formula For...Ch. 4.4 - Objective 4: Apply the Change-of-Base Formula For...Ch. 4.4 - Objective 4: Apply the Change-of-Base Formula For...Ch. 4.4 - Prob. 82PECh. 4.4 - Objective 4: Apply the Change-of-Base Formula For...Ch. 4.4 - Prob. 84PECh. 4.4 - Prob. 85PECh. 4.4 - Prob. 86PECh. 4.4 - Prob. 87PECh. 4.4 - Prob. 88PECh. 4.4 - Prob. 89PECh. 4.4 - Mixed Exercises
For Exercises 89-98, determine if...Ch. 4.4 - Prob. 91PECh. 4.4 - Mixed Exercises For Exercises 89-98, determine if...Ch. 4.4 - Prob. 93PECh. 4.4 - Prob. 94PECh. 4.4 - Prob. 95PECh. 4.4 - Mixed Exercises For Exercises 89-98, determine if...Ch. 4.4 - Prob. 97PECh. 4.4 - Prob. 98PECh. 4.4 - Prob. 99PECh. 4.4 - Prob. 100PECh. 4.4 - Prob. 101PECh. 4.4 - Prob. 102PECh. 4.4 - Prob. 103PECh. 4.4 - Prob. 104PECh. 4.4 - Prob. 105PECh. 4.4 - Prob. 106PECh. 4.4 - Prob. 107PECh. 4.4 - Prob. 108PECh. 4.4 - Prob. 109PECh. 4.4 - Prob. 110PECh. 4.4 - Prob. 111PECh. 4.4 - Prob. 112PECh. 4.4 - Prob. 113PECh. 4.4 - Prob. 114PECh. 4.5 - Skill Practice Solve. a. 42x3=64 b. 272w+5=(13)25wCh. 4.5 - Skill Practice Solve. 5x=83Ch. 4.5 - Prob. 3SPCh. 4.5 - Prob. 4SPCh. 4.5 - Skill Practice
5. Solve.
Ch. 4.5 - Skill Practice
6. Solve.
Ch. 4.5 - Prob. 7SPCh. 4.5 - Prob. 8SPCh. 4.5 - Prob. 9SPCh. 4.5 - Prob. 10SPCh. 4.5 - Skill Practice Determine how long it will take...Ch. 4.5 - Skill Practice
12. a. Find the intensity of sound...Ch. 4.5 - Prob. 1PECh. 4.5 - Prob. 2PECh. 4.5 - Prob. 3PECh. 4.5 - Prob. 4PECh. 4.5 - Prob. 5PECh. 4.5 - Prob. 6PECh. 4.5 - Prob. 7PECh. 4.5 - Prob. 8PECh. 4.5 - Prob. 9PECh. 4.5 - Prob. 10PECh. 4.5 - For Exercises 5 – 16, solve the equation. (See...Ch. 4.5 - For Exercises 5 16, solve the equation. (See...Ch. 4.5 - For Exercises 5 16, solve the equation. (See...Ch. 4.5 - For Exercises 5 16, solve the equation. (See...Ch. 4.5 - For Exercises 5 – 16, solve the equation. (See...Ch. 4.5 - Prob. 16PECh. 4.5 - For Exercises 5 – 16, solve the equation. (See...Ch. 4.5 - For Exercises 5 – 16, solve the equation. (See...Ch. 4.5 - For Exercises 5 16, solve the equation. (See...Ch. 4.5 - For Exercises 5 – 16, solve the equation. (See...Ch. 4.5 - For Exercises 5 16, solve the equation. (See...Ch. 4.5 - Prob. 22PECh. 4.5 - For Exercises 17-34, solve the equation. Write the...Ch. 4.5 - Prob. 24PECh. 4.5 - For Exercises 17-34, solve the equation. Write the...Ch. 4.5 - Prob. 26PECh. 4.5 - For Exercises 17-34, solve the equation. Write the...Ch. 4.5 - Prob. 28PECh. 4.5 - For Exercises 17-34, solve the equation. Write the...Ch. 4.5 - Prob. 30PECh. 4.5 - For Exercises 17-34, solve the equation. Write the...Ch. 4.5 - For Exercises 17-34, solve the equation. Write the...Ch. 4.5 - For Exercises 17-34, solve the equation. Write the...Ch. 4.5 - Prob. 34PECh. 4.5 - For Exercises 17-34, solve the equation. Write the...Ch. 4.5 - Prob. 36PECh. 4.5 - For Exercises 17-34, solve the equation. Write the...Ch. 4.5 - Prob. 38PECh. 4.5 - For Exercises 35-36, determine if the given value...Ch. 4.5 - Prob. 40PECh. 4.5 - For Exercises 37-60, solve the equation. Write the...Ch. 4.5 - Prob. 42PECh. 4.5 - For Exercises 37-60, solve the equation. Write the...Ch. 4.5 - For Exercises 37-60, solve the equation. Write the...Ch. 4.5 - For Exercises 41-62, solve the equation. Write the...Ch. 4.5 - Prob. 46PECh. 4.5 - Prob. 47PECh. 4.5 - Prob. 48PECh. 4.5 - For Exercises 37-60, solve the equation. Write the...Ch. 4.5 - Prob. 50PECh. 4.5 - For Exercises 37-60, solve the equation. Write the...Ch. 4.5 - For Exercises 37-60, solve the equation. Write the...Ch. 4.5 - For Exercises 37-60, solve the equation. Write the...Ch. 4.5 - Prob. 54PECh. 4.5 - For Exercises 37-60, solve the equation. Write the...Ch. 4.5 - Prob. 56PECh. 4.5 - For Exercises 37-60, solve the equation. Write the...Ch. 4.5 - For Exercises 37-60, solve the equation. Write the...Ch. 4.5 - For Exercises 37-60, solve the equation. Write the...Ch. 4.5 - Prob. 60PECh. 4.5 - For Exercises 37-60, solve the equation. Write the...Ch. 4.5 - Prob. 62PECh. 4.5 - For Exercises 61-70, use the model A=Pert or...Ch. 4.5 - Prob. 64PECh. 4.5 - For Exercises 61-70, use the model or , where A...Ch. 4.5 - Prob. 66PECh. 4.5 - Physicians often treat thyroid cancer with a...Ch. 4.5 - Prob. 68PECh. 4.5 - Prob. 69PECh. 4.5 - Sunlight is absorbed in water, and as a result the...Ch. 4.5 - Sunlight is absorbed in water, and as a result the...Ch. 4.5 - Prob. 72PECh. 4.5 - 77. Forge welding is a process in which two pieces...Ch. 4.5 - 78. A pie comes out of the oven at 325°F and is...Ch. 4.5 - Prob. 75PECh. 4.5 - For Exercises 79-80, the formula L=10log(II0)...Ch. 4.5 - Prob. 77PECh. 4.5 - Prob. 78PECh. 4.5 - For Exercises 8182, use the formula pH=-log[H+] ....Ch. 4.5 - For Exercises 8182, use the formula pH=-log[H+] ....Ch. 4.5 - Prob. 81PECh. 4.5 - A company spends x hundred dollars on an...Ch. 4.5 - Prob. 83PECh. 4.5 - On August 31, 1854, an epidemic of cholera was...Ch. 4.5 - Prob. 85PECh. 4.5 - For Exercises 87-94, find an equation for the...Ch. 4.5 - For Exercises 87-94, find an equation for the...Ch. 4.5 - For Exercises 87-94, find an equation for the...Ch. 4.5 - For Exercises 87-94, find an equation for the...Ch. 4.5 - For Exercises 87-94, find an equation for the...Ch. 4.5 - For Exercises 87-94, find an equation for the...Ch. 4.5 - For Exercises 87-94, find an equation for the...Ch. 4.5 - For Exercises 95-112, solve the equation. Write...Ch. 4.5 - For Exercises 95-112, solve the equation. Write...Ch. 4.5 - For Exercises 95-112, solve the equation. Write...Ch. 4.5 - For Exercises 95-112, solve the equation. Write...Ch. 4.5 - For Exercises 95-112, solve the equation. Write...Ch. 4.5 - For Exercises 95-112, solve the equation. Write...Ch. 4.5 - For Exercises 95-112, solve the equation. Write...Ch. 4.5 - For Exercises 95-112, solve the equation. Write...Ch. 4.5 - For Exercises 95-112, solve the equation. Write...Ch. 4.5 - For Exercises 95-112, solve the equation. Write...Ch. 4.5 - Prob. 103PECh. 4.5 - Prob. 104PECh. 4.5 - Prob. 105PECh. 4.5 - For Exercises 95-112, solve the equation. Write...Ch. 4.5 - Prob. 107PECh. 4.5 - Prob. 108PECh. 4.5 - Prob. 109PECh. 4.5 - Prob. 110PECh. 4.5 - Prob. 111PECh. 4.5 - Prob. 112PECh. 4.5 - Prob. 113PECh. 4.5 - Prob. 114PECh. 4.5 - Prob. 115PECh. 4.5 - Prob. 116PECh. 4.5 - Prob. 117PECh. 4.5 - Prob. 118PECh. 4.5 - Prob. 119PECh. 4.5 - Prob. 120PECh. 4.5 - Prob. 121PECh. 4.5 - Prob. 122PECh. 4.5 - Prob. 123PECh. 4.5 - Prob. 124PECh. 4.5 - Prob. 125PECh. 4.5 - Prob. 126PECh. 4.5 - For Exercises 127–130, an equation is given in the...Ch. 4.5 - Prob. 128PECh. 4.5 - Prob. 129PECh. 4.5 - Prob. 130PECh. 4.6 - Skill Practice a. Given T=78+272ekt, solve for k....Ch. 4.6 - Skill Practice Suppose that $10,000 is invested...Ch. 4.6 - Prob. 3SPCh. 4.6 - Prob. 4SPCh. 4.6 - Prob. 5SPCh. 4.6 - Prob. 6SPCh. 4.6 - Prob. 7SPCh. 4.6 - Prob. 8SPCh. 4.6 - Prob. 1PECh. 4.6 - Prob. 2PECh. 4.6 - Prob. 3PECh. 4.6 - Prob. 4PECh. 4.6 - Prob. 5PECh. 4.6 - Prob. 6PECh. 4.6 - Prob. 7PECh. 4.6 - Prob. 8PECh. 4.6 - Prob. 9PECh. 4.6 - Prob. 10PECh. 4.6 - A function defined by y=c1+aebt is called a...Ch. 4.6 - Prob. 12PECh. 4.6 - Prob. 13PECh. 4.6 - Prob. 14PECh. 4.6 - For Exercises 5-14, solve for the indicated...Ch. 4.6 - Prob. 16PECh. 4.6 - Prob. 17PECh. 4.6 - For Exercises 5-14, solve for the indicated...Ch. 4.6 - Prob. 19PECh. 4.6 - For Exercises 5-14, solve for the indicated...Ch. 4.6 - Prob. 21PECh. 4.6 - For Exercises 5-14, solve for the indicated...Ch. 4.6 - Suppose that $12,000 is invested in a bond fund...Ch. 4.6 - 16. Suppose that $50,000 from a retirement account...Ch. 4.6 - Suppose that P dollars in principal is invested in...Ch. 4.6 - Suppose that P dollars in principal is invested in...Ch. 4.6 - The populations of two countries are given for...Ch. 4.6 - The populations of two countries are given for...Ch. 4.6 - A function of the form P(t)=abt represents the...Ch. 4.6 - Prob. 30PECh. 4.6 - For Exercises 23-24, refer to the model used in...Ch. 4.6 - Prob. 32PECh. 4.6 - 25. The isotope of plutonium is used to make...Ch. 4.6 - Prob. 34PECh. 4.6 - Prob. 35PECh. 4.6 - Prob. 36PECh. 4.6 - Prob. 37PECh. 4.6 - The half-life of radium-226 is 1620 yr. Given a...Ch. 4.6 - 31. The population of the United States (in...Ch. 4.6 - Prob. 40PECh. 4.6 - The number of computers N(t) (in millions)...Ch. 4.6 - 34. After a new product is launched the cumulative...Ch. 4.6 - Objective 4: Create Exponential and Logarithmic...Ch. 4.6 - Objective 4: Create Exponential and Logarithmic...Ch. 4.6 - Prob. 45PECh. 4.6 - Prob. 46PECh. 4.6 - Prob. 47PECh. 4.6 - Prob. 48PECh. 4.6 - Prob. 49PECh. 4.6 - Prob. 50PECh. 4.6 - Prob. 51PECh. 4.6 - Prob. 52PECh. 4.6 - Prob. 53PECh. 4.6 - For Exercises 39-46, a table of data is...Ch. 4.6 - Prob. 55PECh. 4.6 - The monthly costs for a small company to do...Ch. 4.6 - 49. The age of a tree t (in yr) and its...Ch. 4.6 - The sales of a book tend to increase over the...Ch. 4.6 - A van is purchased new for $29,200. a. Write a...Ch. 4.6 - Prob. 60PECh. 4.6 - Prob. 61PECh. 4.6 - How does the average rate of change differ for a...Ch. 4.6 - Explain the difference between an exponential...Ch. 4.6 - 56. Explain how to convert an exponential...Ch. 4.6 - Prob. 65PECh. 4.6 - Prob. 66PECh. 4.6 - Prob. 67PECh. 4 - For Exercises 1-2, determine if the relation...Ch. 4 - Prob. 2RECh. 4 - Prob. 3RECh. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - Prob. 6RECh. 4 - Prob. 7RECh. 4 - For Exercises 7-8, a one-to-one function is given....Ch. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Prob. 11RECh. 4 - Prob. 12RECh. 4 - Prob. 13RECh. 4 - Prob. 14RECh. 4 - Prob. 15RECh. 4 - Prob. 16RECh. 4 - Prob. 17RECh. 4 - Prob. 18RECh. 4 - For Exercises 18-19, use the formulas on page 420....Ch. 4 - 20. A patient is treated with 128 mCi...Ch. 4 - Prob. 21RECh. 4 - Prob. 22RECh. 4 - Prob. 23RECh. 4 - Prob. 24RECh. 4 - Prob. 25RECh. 4 - Prob. 26RECh. 4 - Prob. 27RECh. 4 - Prob. 28RECh. 4 - Prob. 29RECh. 4 - Prob. 30RECh. 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 - For Exercise 40-41, use the formula pH = – log...Ch. 4 - For Exercise 40-41, use the formula pH = – log...Ch. 4 - Prob. 42RECh. 4 - Prob. 43RECh. 4 - Prob. 44RECh. 4 - Prob. 45RECh. 4 - Prob. 46RECh. 4 - Prob. 47RECh. 4 - Prob. 48RECh. 4 - Prob. 49RECh. 4 - Prob. 50RECh. 4 - Prob. 51RECh. 4 - Prob. 52RECh. 4 - For Exercises 53-55, write the logarithmic...Ch. 4 - Prob. 54RECh. 4 - Prob. 55RECh. 4 - Prob. 56RECh. 4 - Prob. 57RECh. 4 - For Exercises 56- 58, use , and to approximate...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 - For Exercises 61-80, solve the equation. Write the...Ch. 4 - Prob. 69RECh. 4 - Prob. 70RECh. 4 - Prob. 71RECh. 4 - Prob. 72RECh. 4 - Prob. 73RECh. 4 - Prob. 74RECh. 4 - Prob. 75RECh. 4 - Prob. 76RECh. 4 - Prob. 77RECh. 4 - For Exercises 61-80, solve the equation. Write the...Ch. 4 - Prob. 79RECh. 4 - Prob. 80RECh. 4 - Prob. 81RECh. 4 - Prob. 82RECh. 4 - 83. The percentage of visible light P (in decimal...Ch. 4 - Prob. 84RECh. 4 - Prob. 85RECh. 4 - Prob. 86RECh. 4 - The population of Germany in 2011 was...Ch. 4 - The population of Chile was approximately 16.9...Ch. 4 - 89. A sample from human remains found near...Ch. 4 - 90. A lake is stocked with bass by the U.S. Park...Ch. 4 - Prob. 91RECh. 4 - Prob. 92RECh. 4 - Prob. 1TCh. 4 - Prob. 2TCh. 4 - Given f(x)=x+3x4, write an equation for the...Ch. 4 - Prob. 4TCh. 4 - Prob. 5TCh. 4 - Prob. 6TCh. 4 - Prob. 7TCh. 4 - Prob. 8TCh. 4 - Prob. 9TCh. 4 - For Exercises 8-11,
a. Graph the...Ch. 4 - Write the statement in exponential form. ln(x+y)=aCh. 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 - For Exercises 19-20, write the domain of the...Ch. 4 - For Exercises 21-22, write the logarithm as a sum...Ch. 4 - Prob. 22TCh. 4 - For Exercises 23-24, write the logarithmic...Ch. 4 - Prob. 24TCh. 4 - Prob. 25TCh. 4 - Prob. 26TCh. 4 - Prob. 27TCh. 4 - For Exercises 27-36, solve the equation. Write the...Ch. 4 - For Exercises 27-36, solve the equation. Write the...Ch. 4 - Prob. 30TCh. 4 - For Exercises 27-36, solve the equation. Write the...Ch. 4 - For Exercises 27-36, solve the equation. Write the...Ch. 4 - For Exercises 27-36, solve the equation. Write the...Ch. 4 - For Exercises 27-36, solve the equation. Write the...Ch. 4 - For Exercises 27-36, solve the equation. Write the...Ch. 4 - Prob. 36TCh. 4 - Prob. 37TCh. 4 - Prob. 38TCh. 4 - Prob. 39TCh. 4 - Prob. 40TCh. 4 - 41. The population of a herd of deer on an island...Ch. 4 - Prob. 42TCh. 4 - Prob. 1CRECh. 4 - Prob. 2CRECh. 4 - Prob. 3CRECh. 4 - Prob. 4CRECh. 4 - Prob. 5CRECh. 4 - Prob. 6CRECh. 4 - Prob. 7CRECh. 4 - For Exercises 5-13, solve the equations and...Ch. 4 - Prob. 9CRECh. 4 - Prob. 10CRECh. 4 - Prob. 11CRECh. 4 - Prob. 12CRECh. 4 - For Exercises 5-13, solve the equations and...Ch. 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
- DICUSS DISCOVER: The Number of Digits in an integer Compare log1000 to the number of digits in 1000. Do the same for 10,000. How many digits does any number between 1000and10, 000 have? Between what two values must the common logarithm of such a number lie? Use your observations to explain why the number of digits in any positive integer xislogx+1. The symbol n is the greatest integer function defined in Section 2.2. How many digits does the number 2100 have?arrow_forwardThe function f(x)=5x is an exponential function with base______; f(2) =_______, f(0) =______, f(2) =_______, and f(6) =_______.arrow_forwardLakarkan graf fungsi. Sketch the graph of the function: log3(x + 1)arrow_forward
- Write an exponential function that represents a car valued at $12,000, losing 5% of its value each year. O f(x) = 12000(1.05)" O f (x) = 12000(0.95)" O f(x) = 0.95(12000)" 21 22arrow_forwardDoes the rule y=-2-2 represent a linear or ari exponential function? OA exponential B. linear Review progressarrow_forwardState the domain of the function. Show all work. (Precalculus 1 Easy)arrow_forward
- The annual average price per square foot for office space in a city was $30.05 in 2004, and it was $66.78 in 2015 a) Find an exponential function of the form f(t)=y0bt to model these data in which t=0 corresponds to 2004 The first full year in which th eprice per square foot exceeded $49 was___arrow_forwardMAA MATHEMATICAL ASSOCIATION OF AMERICA WeBWorK/2024-FALL-MATH1007-SECTION-C / Assignment 2 / 2 Previous Problem Problem List Next Problem Assignment 2: Problem 2 (1 point) Logged in as Caitlin Armstrong. Log O 10 y -18 -5 1 18 x -5 -10 Given the graph of f(x) above, find the following and write your answer in interval notation: (a) Domain of f(x): (b) Range of f(x): Note: You can earn partial credit on this problem. Preview My Answers Submit Answers 26arrow_forwardHow do you know which statements are true?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY
Solution of Differential Equations and Initial Value Problems; Author: Jefril Amboy;https://www.youtube.com/watch?v=Q68sk7XS-dc;License: Standard YouTube License, CC-BY