   Chapter 4.6, Problem 4CP ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Checkpoint 4 Worked-out solution available at LarsonAppliedCalculus.comUse the model in Example 4 to determine when sales will drop to 50,000 MP3 players.

To determine

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

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 dydt=ky, then y is given by the equation, y=Cekt, 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=Cekt

Here, y=100,000 at t=0

Substitute in the equation y=Cekt.

100000=Cek×0100000=C×1C=100000

Evaluate the value of k by substituting y=80,000 at t=4

80000=100000e4k

Divide each side by 100000 and apply exponential property.

80000100000=e4k810=e4k0.8=e4k

Take natural log on both the sides,

ln(e4k)=ln(0

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