Chapter 8.4, Problem 18E

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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 + 10*e*^{0.8t} 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

Â per week.

Time *t* is measured in weeks.

**Calculation:**

Show the increasing rate of mosquitoes as follows:

Apply Net change Theorem as follows:

The integral of a rate of change is the net change

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.

Substitute 9 for *b*, 5 for *a*, and

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