Explanation Given Information: The balance doubles in 8 years and interest is compounded continuously. Formula used: Exponential growth and decay: If the rate of change of a positive quantity y with respect to time is proportional to the amount of quantity present at any time t , that is d y d t = k y , then y is given by the equation, y = C e k t , where C is the value of the quantity at time t = 0 and k is the constant of proportionality. If k > 0 then there is exponential growth and when k < 0 then there is exponential decay. Calculation: Consider y be the number of MP 3 players at time t and the exponential decay model is y = C e k t Here, y = 100 , 000 at t = 0 Substitute in the equation y = C e k t . 100000 = C e k × 0 100000 = C × 1 C = 100000 Evaluate the value of k by substituting y = 80 , 000 at t = 4 80000 = 100000 e 4 k Divide each side by 100000 and apply exponential property. 80000 100000 = e 4 k 8 10 = e 4 k 0.8 = e 4 k Take natural log on both the sides, ln ( e 4 k ) = ln ( 0

Calculus: An Applied Approach (MindTap Course List)

10th Edition

ISBN: 9781305860919

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 4.6, Problem 4CP

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To calculate: The time when the sales will drop to 50,000 MP 3 players from 100,000 MP 3 players per month using the exponential pattern of decline if after four months of discontinuation of advertisements on national television, the sales have dropped to 80,000 MP 3 players

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Chapter 4.6, Problem 3CP

Chapter 4.6, Problem 1SWU

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Chapter 4 Solutions

Calculus: An Applied Approach (MindTap Course List)

Ch. 4.1 - Use the properties of exponents to simplify each...Ch. 4.1 - Use the properties of exponents to simplify each...Ch. 4.1 - Use the formula for the ratio of carbon isotopes...Ch. 4.1 - Prob. 4CP Ch. 4.1 - Prob. 5CP Ch. 4.1 - Prob. 1SWU Ch. 4.1 - Prob. 2SWU Ch. 4.1 - Prob. 3SWU Ch. 4.1 - Prob. 4SWU Ch. 4.1 - Prob. 5SWU

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The time when the sales will drop to 50 , 000 MP 3 players from 100 , 000 MP 3 players per month using the exponential pattern of decline if after four months of discontinuation of advertisements on national television, the sales have dropped to 80 , 000 MP 3 players

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To calculate: The time when the sales will drop to 50,000 MP 3 players from 100,000 MP 3 players per month using the exponential pattern of decline if after four months of discontinuation of advertisements on national television, the sales have dropped to 80,000 MP 3 players

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