   Chapter 11.5, Problem 101E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Epidemics A flu epidemic described in Example 1 in Section 2.4 approximately followed the curve P = 150 1 + 15 , 000 e − 0.35 t  million people, where P is the number of people infected and t is the number of weeks after the start of the epidemic. How fast is the epidemic growing (that is, how many new cases are there each week) after 20 weeks? After 30 weeks? After 40 weeks? (Round your answers to two significant digits.) [HINT: See Example 3.]

To determine

To calculate: The rate at which the epidemic is growing after 20 weeks, 30 weeks and 40 weeks if the flu epidemic is approximated with the equation P=1501+15,000e0.35tmillion people where P is the number of people infected and t is the number of weeks after the start of the epidemic.

Explanation

Given Information:

The flu epidemic is approximated with the equation P=1501+15,000e0.35tmillion people where P is the number of people infected and t is the number of weeks after the start of the epidemic and the time after which the rate of growth of the epidemic is calculated is 20 weeks, 30 weeks and 40 weeks respectively.

Formula used:

The following derivative formula is used:

ddx(ex)=ex

Calculation:

Consider that the flu epidemic is approximated with the equation P=1501+15,000e0.35tmillion people where P is the number of people infected and t is the number of weeks after the start of the epidemic.

Re-write P=1501+15,000e0.35t as P=150(1+15,000e0.35t)1.

The rate of change of P(t) is equal to the rate at which the epidemic grows.

dPdt=150(1+15,000e0.35t)11[15000(0.35e0.35t)]=150(1+15,000e0.35t)2[15000(0.35e0.35t)]=787500e0.35t(1+15,000e0.35t)2

Substitute t=20 in the equation to calculate the rate at which the epidemic grows after 20 weeks.

P(20)=787500e0.35(20)(1+15,000e0

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