MYLAB MATH COLLEGE ALGEBRA IN CONTEXT
6th Edition
ISBN: 9780135823002
Author: HARSHBARGER
Publisher: PEARSON
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Chapter 5.4, Problem 23E
China’s Shale Natural Gas The estimated annual production of shale natural gas in China for the years 2013 through 2020, in millions of cubic feet, is shown in the table.
- a. Find the equation of the exponential function that models these estimates of the number of millions of cubic feet of shale natural gas in China y as a function of the number of years x after 2010.
- b. Graph the model and the data on the same axes and discuss the fit.
- c. What does the model estimate that the number of millions of cubic feet of shale natural gas in China will be in 2021?
- d. When does the model estimate that the number of millions of cubic feet of shale natural gas in China will be 9506?
(Source: Sanford C. Bernstein)
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1. Abel's Theorem. The goal in this problem is to prove Abel's theorem by following a series of steps
(each step must be justified).
Theorem 0.1 (Abel's Theorem).
If y1 and y2 are solutions of the differential equation
y" + p(t) y′ + q(t) y = 0,
where p and q are continuous on an open interval, then the Wronskian is given by
W (¥1, v2)(t) = c exp(− [p(t) dt),
where C is a constant that does not depend on t. Moreover, either W (y1, y2)(t) = 0 for every t in I or
W (y1, y2)(t) = 0 for every t in I.
1. (a) From the two equations (which follow from the hypotheses),
show that
y" + p(t) y₁ + q(t) y₁ = 0 and y½ + p(t) y2 + q(t) y2 = 0,
2. (b) Observe that
Hence, conclude that
(YY2 - Y1 y2) + P(t) (y₁ Y2 - Y1 Y2) = 0.
W'(y1, y2)(t) = yY2 - Y1 y2-
W' + p(t) W = 0.
3. (c) Use the result from the previous step to complete the proof of the theorem.
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Support Department Cost Allocation—Reciprocal Services Method
Blue Africa Inc. produces laptops and desktop computers. The company’s production activities mainly occur in what the company calls its Laser and Forming departments. The Cafeteria and Security departments support the company’s production activities and allocate costs based on the number of employees and square feet, respectively. The total cost of the Security Department is $261,000. The total cost of the Cafeteria Department is $300,000. The number of employees and the square footage in each department are as follows:
Department
Employees
Square Feet
Security
10
570
Cafeteria
28
2,400
Laser
40
4,800
Forming
50
800
Using the reciprocal services method of support department cost allocation, determine the total costs from the Security Department that should be allocated to…
I need help with this problem and an explanation of the solution for the image described below. (Statistics: Engineering Probabilities)
Chapter 5 Solutions
MYLAB MATH COLLEGE ALGEBRA IN CONTEXT
Ch. 5.1 - Which of the following functions are exponential...Ch. 5.1 - Prob. 2ECh. 5.1 - a. Graph the function f(x) = ex on the window [5,...Ch. 5.1 - a. Graph the function f(x) = 5x on the window [5,...Ch. 5.1 - Graph the function y = 3x on [5, 5] by [10, 30].Ch. 5.1 - Prob. 6ECh. 5.1 - Prob. 7ECh. 5.1 - Prob. 8ECh. 5.1 - Prob. 9ECh. 5.1 - Prob. 10E
Ch. 5.1 - Prob. 11ECh. 5.1 - Prob. 12ECh. 5.1 - Prob. 13ECh. 5.1 - Prob. 14ECh. 5.1 - Prob. 15ECh. 5.1 - Prob. 16ECh. 5.1 - Prob. 17ECh. 5.1 - Prob. 18ECh. 5.1 - Prob. 19ECh. 5.1 - In Exercises 1924, use your knowledge of...Ch. 5.1 - Prob. 21ECh. 5.1 - Prob. 22ECh. 5.1 - Prob. 23ECh. 5.1 - Prob. 24ECh. 5.1 - Prob. 25ECh. 5.1 - Prob. 26ECh. 5.1 - Prob. 27ECh. 5.1 - Prob. 28ECh. 5.1 - Prob. 29ECh. 5.1 - Prob. 30ECh. 5.1 - Prob. 31ECh. 5.1 - Prob. 32ECh. 5.1 - Prob. 33ECh. 5.1 - Prob. 34ECh. 5.1 - Prob. 35ECh. 5.1 - Prob. 36ECh. 5.1 - Prob. 37ECh. 5.1 - Sales Decay At the end of an advertising campaign,...Ch. 5.1 - Investment a. Graph the function S = 80,000...Ch. 5.1 - Investment a. Graph the function S = 56,000...Ch. 5.1 - Prob. 41ECh. 5.1 - Prob. 42ECh. 5.1 - Prob. 43ECh. 5.1 - Prob. 44ECh. 5.1 - Prob. 45ECh. 5.1 - Prob. 46ECh. 5.1 - Prob. 47ECh. 5.1 - Prob. 48ECh. 5.1 - Prob. 49ECh. 5.1 - Prob. 50ECh. 5.1 - Population The population in a certain city was...Ch. 5.1 - Prob. 52ECh. 5.1 - Prob. 53ECh. 5.1 - Drugs in the Bloodstream If a drug is injected...Ch. 5.1 - Prob. 55ECh. 5.1 - Prob. 56ECh. 5.2 - In Exercises 14, write the logarithmic equations...Ch. 5.2 - In Exercises 14, write the logarithmic equations...Ch. 5.2 - y = ln(2x)Ch. 5.2 - Prob. 4ECh. 5.2 - Prob. 5ECh. 5.2 - Prob. 6ECh. 5.2 - Prob. 7ECh. 5.2 - Prob. 8ECh. 5.2 - In Exercises 9 and 10, evaluate the logarithms, if...Ch. 5.2 - In Exercises 9 and 10, evaluate the logarithms, if...Ch. 5.2 - In Exercises 1113, find the value of the...Ch. 5.2 - In Exercises 1113, find the value of the...Ch. 5.2 - Prob. 13ECh. 5.2 - Graph the functions by changing to exponential...Ch. 5.2 - Prob. 15ECh. 5.2 - Prob. 16ECh. 5.2 - Prob. 17ECh. 5.2 - Prob. 18ECh. 5.2 - Prob. 19ECh. 5.2 - Prob. 20ECh. 5.2 - Prob. 21ECh. 5.2 - Prob. 22ECh. 5.2 - Prob. 23ECh. 5.2 - Prob. 24ECh. 5.2 - Prob. 25ECh. 5.2 - Prob. 26ECh. 5.2 - Prob. 27ECh. 5.2 - Prob. 28ECh. 5.2 - Prob. 29ECh. 5.2 - Prob. 30ECh. 5.2 - Prob. 31ECh. 5.2 - Prob. 32ECh. 5.2 - In Exercises 3134, rewrite each expression as a...Ch. 5.2 - In Exercises 3134, rewrite each expression as a...Ch. 5.2 - Prob. 35ECh. 5.2 - Prob. 36ECh. 5.2 - Prob. 37ECh. 5.2 - In Exercises 3538, rewrite each expression as a...Ch. 5.2 - Prob. 39ECh. 5.2 - Prob. 40ECh. 5.2 - Prob. 41ECh. 5.2 - Prob. 42ECh. 5.2 - Prob. 43ECh. 5.2 - Prob. 44ECh. 5.2 - Prob. 45ECh. 5.2 - Obesity The percent of Americas who are obese from...Ch. 5.2 - Doubling Time If 4000 is invested in an account...Ch. 5.2 - Prob. 48ECh. 5.2 - Prob. 49ECh. 5.2 - Prob. 50ECh. 5.2 - Prob. 51ECh. 5.2 - Prob. 52ECh. 5.2 - Earthquakes If an earthquake has an intensity of...Ch. 5.2 - Earthquakes a. If an earthquake has an intensity...Ch. 5.2 - Prob. 55ECh. 5.2 - Prob. 56ECh. 5.2 - Prob. 57ECh. 5.2 - Earthquakes On January 9, 2008, an earthquake in...Ch. 5.2 - Prob. 59ECh. 5.2 - Prob. 60ECh. 5.2 - Prob. 61ECh. 5.2 - Prob. 62ECh. 5.2 - Use the following information to answer the...Ch. 5.2 - Prob. 64ECh. 5.2 - Prob. 65ECh. 5.2 - Prob. 66ECh. 5.2 - Use the following information to answer the...Ch. 5.2 - Prob. 68ECh. 5.2 - pH Levels The pH value of eggs is 7.79. Find the...Ch. 5.2 - To answer the questions in Exercises 6872, use the...Ch. 5.2 - Prob. 71ECh. 5.2 - Prob. 72ECh. 5.3 - In Exercises 110, solve the equations...Ch. 5.3 - Prob. 2ECh. 5.3 - Prob. 3ECh. 5.3 - Prob. 4ECh. 5.3 - Prob. 5ECh. 5.3 - Prob. 6ECh. 5.3 - Prob. 7ECh. 5.3 - Prob. 8ECh. 5.3 - Prob. 9ECh. 5.3 - Prob. 10ECh. 5.3 - Prob. 11ECh. 5.3 - Prob. 12ECh. 5.3 - Prob. 13ECh. 5.3 - Prob. 14ECh. 5.3 - Prob. 15ECh. 5.3 - Prob. 16ECh. 5.3 - Prob. 17ECh. 5.3 - Prob. 18ECh. 5.3 - Prob. 19ECh. 5.3 - Prob. 20ECh. 5.3 - Prob. 21ECh. 5.3 - Prob. 22ECh. 5.3 - Prob. 23ECh. 5.3 - Prob. 24ECh. 5.3 - Prob. 25ECh. 5.3 - Prob. 26ECh. 5.3 - Prob. 27ECh. 5.3 - Prob. 28ECh. 5.3 - Prob. 29ECh. 5.3 - Prob. 30ECh. 5.3 - Prob. 31ECh. 5.3 - Prob. 32ECh. 5.3 - Prob. 33ECh. 5.3 - Prob. 34ECh. 5.3 - Prob. 35ECh. 5.3 - Prob. 36ECh. 5.3 - Prob. 37ECh. 5.3 - Prob. 38ECh. 5.3 - Prob. 39ECh. 5.3 - Prob. 40ECh. 5.3 - Prob. 41ECh. 5.3 - Prob. 42ECh. 5.3 - Sales Decay After a television advertising...Ch. 5.3 - Prob. 44ECh. 5.3 - Prob. 45ECh. 5.3 - Prob. 46ECh. 5.3 - Super Bowl Ads A minute ad during Super Bowl VII...Ch. 5.3 - Prob. 48ECh. 5.3 - Purchasing Power The purchasing power (real value...Ch. 5.3 - Prob. 50ECh. 5.3 - Prob. 51ECh. 5.3 - Real Estate Inflation During a 10-year period of...Ch. 5.3 - Prob. 53ECh. 5.3 - Prob. 54ECh. 5.3 - Drugs in the Bloodstream The concentration of a...Ch. 5.3 - Prob. 56ECh. 5.3 - Prob. 57ECh. 5.3 - Prob. 58ECh. 5.3 - Prob. 59ECh. 5.3 - Prob. 60ECh. 5.3 - Prob. 61ECh. 5.3 - Prob. 62ECh. 5.3 - Prob. 63ECh. 5.3 - Prob. 64ECh. 5.3 - Prob. 65ECh. 5.3 - Prob. 66ECh. 5.3 - Prob. 67ECh. 5.3 - Prob. 68ECh. 5.3 - Prob. 69ECh. 5.3 - Prob. 70ECh. 5.3 - Prob. 71ECh. 5.3 - Prob. 72ECh. 5.3 - Prob. 73ECh. 5.3 - Prob. 74ECh. 5.3 - Prob. 75ECh. 5.3 - Prob. 76ECh. 5.3 - Prob. 77ECh. 5.3 - Prob. 78ECh. 5.3 - Prob. 79ECh. 5.3 - Drugs in the Bloodstream The concentration of a...Ch. 5.3 - Carbon-14 Dating An exponential decay function can...Ch. 5.3 - Sales Decay After a television advertising...Ch. 5.3 - Prob. 83ECh. 5.4 - Find the exponential function that models the data...Ch. 5.4 - Prob. 2ECh. 5.4 - Prob. 3ECh. 5.4 - The following table has input x and output h(x)....Ch. 5.4 - Prob. 5ECh. 5.4 - Find the exponential function that is the best fit...Ch. 5.4 - Prob. 7ECh. 5.4 - Prob. 8ECh. 5.4 - Compare the first differences and the percent...Ch. 5.4 - Prob. 10ECh. 5.4 - Prob. 11ECh. 5.4 - Prob. 12ECh. 5.4 - Prob. 13ECh. 5.4 - Prob. 14ECh. 5.4 - a. Make a scatter plot of the data in the table...Ch. 5.4 - Prob. 16ECh. 5.4 - Prob. 17ECh. 5.4 - Use the exponential form y = a (1 + r)x to model...Ch. 5.4 - Prob. 19ECh. 5.4 - Prob. 20ECh. 5.4 - Prob. 21ECh. 5.4 - Prob. 22ECh. 5.4 - Chinas Shale Natural Gas The estimated annual...Ch. 5.4 - Prob. 24ECh. 5.4 - Average Annual Wage The following table shows the...Ch. 5.4 - Alzheimers Disease Partially because people in the...Ch. 5.4 - Prob. 27ECh. 5.4 - Prob. 28ECh. 5.4 - Prob. 29ECh. 5.4 - Prob. 30ECh. 5.4 - Prob. 31ECh. 5.4 - Prob. 32ECh. 5.4 - Prob. 33ECh. 5.4 - Sexually Active Boys The percents of boys age x or...Ch. 5.4 - Fuel Economy The lifetime gasoline use of...Ch. 5.4 - National Debt The table gives the U.S. national...Ch. 5.5 - Evaluate the expressions in Exercises 110. 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Solve S =...Ch. 5.6 - Prob. 2ECh. 5.6 - Prob. 3ECh. 5.6 - Prob. 4ECh. 5.6 - Prob. 5ECh. 5.6 - Prob. 6ECh. 5.6 - IRA Anne Wright decides to invest 4000 in an IRA...Ch. 5.6 - Prob. 8ECh. 5.6 - Prob. 9ECh. 5.6 - Prob. 10ECh. 5.6 - Prob. 11ECh. 5.6 - Prob. 12ECh. 5.6 - Prob. 13ECh. 5.6 - Prob. 14ECh. 5.6 - Annuities Find the present value of an annuity...Ch. 5.6 - Prob. 16ECh. 5.6 - Prob. 17ECh. 5.6 - College Tuition A couple wants to establish a fund...Ch. 5.6 - Insurance Payment A man is disabled in an accident...Ch. 5.6 - Auto Leasing A woman wants to lease rather than...Ch. 5.6 - Business Sale A man can sell his Thrifty...Ch. 5.6 - Prob. 22ECh. 5.6 - Home Mortgage A couple wants to buy a house and...Ch. 5.6 - Prob. 24ECh. 5.6 - Loan Repayment A loan of 10,000 is to be amortized...Ch. 5.6 - Prob. 26ECh. 5.6 - Home Mortgage A couple who wants to purchase a...Ch. 5.6 - Prob. 28ECh. 5.7 - Give approximate answers to two decimal places. 1....Ch. 5.7 - Prob. 2ECh. 5.7 - Prob. 3ECh. 5.7 - Prob. 4ECh. 5.7 - Give approximate answers to two decimal places. 5....Ch. 5.7 - Prob. 6ECh. 5.7 - Give approximate answers to two decimal places. 7....Ch. 5.7 - Prob. 8ECh. 5.7 - Spread of a Disease The spread of a highly...Ch. 5.7 - Prob. 10ECh. 5.7 - Prob. 11ECh. 5.7 - Prob. 12ECh. 5.7 - Spread of a Rumor The number of people in a small...Ch. 5.7 - Organizational Growth A new community college...Ch. 5.7 - Prob. 22ECh. 5.7 - Prob. 23ECh. 5.7 - Company Growth Because of a new research grant,...Ch. 5.7 - Prob. 25ECh. 5.7 - Prob. 26ECh. 5.7 - Prob. 27ECh. 5.7 - Prob. 28ECh. 5.7 - Prob. 29ECh. 5.7 - Prob. 30ECh. 5 - In Exercises 1 and 2, use the properties of...Ch. 5 - a. y5 y b. w10w4 c. (6bx)3 d. (5z2)3 e. 32 33 f....Ch. 5 - In Exercises 318, use the properties of exponents...Ch. 5 - Prob. 4TECh. 5 - Prob. 5TECh. 5 - Prob. 6TECh. 5 - Prob. 7TECh. 5 - Prob. 8TECh. 5 - Prob. 9TECh. 5 - In Exercises 318, use the properties of exponents...Ch. 5 - Prob. 11TECh. 5 - Prob. 12TECh. 5 - Prob. 13TECh. 5 - Prob. 14TECh. 5 - Prob. 15TECh. 5 - Prob. 16TECh. 5 - Prob. 17TECh. 5 - Prob. 18TECh. 5 - In Exercises 1922, write the numbers in scientific...Ch. 5 - Prob. 20TECh. 5 - Prob. 21TECh. 5 - In Exercises 1922, write the numbers in scientific...Ch. 5 - Prob. 23TECh. 5 - Prob. 24TECh. 5 - Prob. 25TECh. 5 - Prob. 26TECh. 5 - Prob. 27TECh. 5 - Prob. 28TECh. 5 - In Exercises 2938, use the properties of exponents...Ch. 5 - Prob. 30TECh. 5 - Prob. 31TECh. 5 - Prob. 32TECh. 5 - Prob. 33TECh. 5 - Prob. 34TECh. 5 - Prob. 35TECh. 5 - Prob. 36TECh. 5 - Prob. 37TECh. 5 - Prob. 38TECh. 5 - Prob. 1RECh. 5 - Prob. 2RECh. 5 - Prob. 3RECh. 5 - Prob. 4RECh. 5 - Prob. 5RECh. 5 - Prob. 6RECh. 5 - Prob. 7RECh. 5 - Prob. 8RECh. 5 - Prob. 9RECh. 5 - Prob. 10RECh. 5 - In Exercises 1012, write the logarithmic equations...Ch. 5 - In Exercises 1012, write the logarithmic equations...Ch. 5 - Write the inverse of y = 4x in logarithmic form.Ch. 5 - In Exercises 1416, evaluate the logarithms, if...Ch. 5 - In Exercises 1416, evaluate the logarithms, if...Ch. 5 - Prob. 16RECh. 5 - Prob. 17RECh. 5 - Prob. 18RECh. 5 - In Exercises 1719, find the value of the...Ch. 5 - In Exercises 20 and 21, use a change of base...Ch. 5 - Prob. 21RECh. 5 - Prob. 22RECh. 5 - Prob. 23RECh. 5 - Prob. 24RECh. 5 - Prob. 25RECh. 5 - In Exercises 2427, solve the exponential...Ch. 5 - In Exercises 2427, solve the exponential...Ch. 5 - Prob. 28RECh. 5 - Rewrite 6 log4 x 2 log4 y as a single logarithm.Ch. 5 - Determine whether a linear or an exponential...Ch. 5 - Evaluate P(1+rk)kn for P = 1000, r = 8%, k = 12, n...Ch. 5 - Prob. 32RECh. 5 - Prob. 33RECh. 5 - a. Graph y = 500 (0.10.2x) for x = 0 to x = 10. b....Ch. 5 - Prob. 35RECh. 5 - Prob. 36RECh. 5 - Sales Decay At the end of an advertising campaign,...Ch. 5 - Earthquakes a. 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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