   Chapter 8.4, Problem 18E

Chapter
Section
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)

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Let f(x)={2x+1if1x0x2+2if0x2 Find (a) f(1), (b) f(0), and (c) f(32).

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

In Exercises 1728, use the logarithm identities to obtain the missing quantity.

Finite Mathematics and Applied Calculus (MindTap Course List)

Find the general indefinite integral. sect(sect+tant)dt

Single Variable Calculus: Early Transcendentals, Volume I

The length of the are r = e for 0 is given by: a) 0ed b) 02e2d c) 02ed d) 02ed

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

True or False: If F is conservative, then curl F = 0.

Study Guide for Stewart's Multivariable Calculus, 8th 