# Starting with an initial value of P(0) = 30, the population of a prairie dog community grows at a...

## Question:

Starting with an initial value of P(0) = 30, the population of a prairie dog community grows at a rate of {eq}P'(t) = 40 - \frac{t}{2} {/eq} (in units of prairie dogs/month), for {eq}0 \leq t \leq 80 {/eq}.

A) What is the population 14 months later?

B) Find the population P(t) for {eq}0 \leq t \leq 80 {/eq}.

## Rate of Population Growth

The growth of a population entails how a certain population increase or decrease with respect to time. From the rate of the population growth, the number of the population can be determined by integration of the rate function and then applying the initial conditions.

We can determine the population of the prairie dog community, given the rate {eq}P'(t) {/eq}, by integrating the rate with respect to time. This...

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