# If the instantaneous rate of change of a population is #50t^2 - 100t^(3/2)# (measured in individuals per year) and the initial population is 25000 then what is the population after t years?

##### 1 Answer

To answer this question, you need to find a particular antiderivative.

Let

We are told that the population is changing at a rate -- stop! that means we're going to be told something about the derivative (the rate of change).

The population is changing at a rate of

This tells us that

Our task is to find

If

So

We also know that

I think writing all of the following clutters up the work:

To find the antiderivative of

(dividing is multiplying by the reciprocal.)