   Chapter 2.2, Problem 78E 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

Flies Flies in Suffolk County have been breeding like frogs! Three years ago, the Health Commission caught 4,000 flies in a trap in 1 hour. This year, it caught 7,000 flies in 1 hour.a. Find an exponential model for the fly population.b. Assuming exponential population growth, how many flies should the commission expect to catch next year?

(a)

To determine

The exponential growth model of the fly population if their population grew from 4000 to 7000 in 1 years.

Explanation

Given Information:

The initial population was 4000 two years ago and present population is 7000.

Consider the following formula of exponential function,

P(t)=Abt

Here P(t) is fly population as a function of time t, A,b are constant and t is time since 1 years ago.

Initially population was 4000 one years ago

Substitute t=0 in the equation P(t)=Abt.

P(0)=Ab0

Substitute P(0)=4000 and b0=1 in the equation P(0)=Ab0.

4000=A

Now, the fly population grew from 4000 to 7000 in 1 years.

For 3 years ago, the time difference is 3,

Substitute t=3 in the equation P(t)=Abt.

P(3)=Ab3

Substitute P(3)=7000 and A=4000 in the equation P(3)=Ab3

(b)

To determine

The number of flies that the commission is expected to catch next year if fly population grew from 4000 to 7000 in 1 years.

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