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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem

A hot, wet summer is causing a mosquito population explosion in a lake resort area. The number of mosquitoes is increasing at an estimated rate of 2200 + 10e0.8t per week (where t is measured in weeks). By how much does the mosquito population increase between the fifth and ninth weeks of summer?

To determine

To calculate: increased mosquito population during fifth and ninth weeks of summer.

Explanation

Given information:

The number of mosquitoes is increasing at an estimated rate of (2,200+10e0.8t)

 per week.

Time t is measured in weeks.

Calculation:

Show the increasing rate of mosquitoes as follows:

n(t)=2,200+10e0.8t

Apply Net change Theorem as follows:

The integral of a rate of change is the net change

abF(x)dx=F(b)F(a) (1)

Here, the lower limit is a and the upper limit is b.

Apply Net Change Theorem to calculate the number of mosquito population increase between fifth and ninth weeks of summer.

Modify Equation (1) for the calculation of capital number of mosquito population increase.

abn(t)dt=n(b)n(a) (2)

Substitute 9 for b, 5 for a, and (2,200+10e0.8t) for n(t) in Equation (2)

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