Question
Asked Mar 4, 2020
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A study indicates that t months from now the population of a certain town will
change at the rate of P'(t) = 5+ Vt² people per month.
3
1) What is the current rate of change? Is the population increasing or a decreasing?
2) What will be the rate of change in 8 months? Is the population increasing or decreasing?
3) By how much will the population increase or decrease over the next 8 months?
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A study indicates that t months from now the population of a certain town will change at the rate of P'(t) = 5+ Vt² people per month. 3 1) What is the current rate of change? Is the population increasing or a decreasing? 2) What will be the rate of change in 8 months? Is the population increasing or decreasing? 3) By how much will the population increase or decrease over the next 8 months?

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Expert Answer

Step 1

To determine the rate of change.

Step 2

Given:

Calculus homework question answer, step 2, image 1

Step 3

(1)

For current rate of change comput P'(0) as,

Calculus homework question answer, step 3, image 1

Since, P'(t) > 0 for t > 0 hence the population is increasing.

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