   Chapter 4.6, Problem 2CP ### 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 2 Worked-out solution available at LarsonAppliedCalculus.comFind the exponential growth model for a population of fruit flies for which there are 100 flies after 2 days and 400 flies after 4 days.

To determine

To calculate: The exponential growth model for a population if the number of fruit flies are 100 after 2 days and after 4 days, there are 400 flies.

Explanation

Given Information:

The number of fruit flies are 100 after 2 days and after 4 days, there are 400 flies.

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 flies at time t,

Here, y=100 at t=2 and y=400 at t=4

Substitute in the equation y=Cekt.

100=Ce2k400=Ce4k

Evaluate the value of C from first equation.

100=Ce2kC=100e2k

Substitute the value of C in second equation.

400=(100e2k)e4k

Divide each side by 100 and apply exponential property

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