009B Sample Midterm 1, Problem 3

A population grows at a rate

$P'(t)=500e^{-t}$

where  $P(t)$  is the population after  $t$  months.

(a)   Find a formula for the population size after  $t$  months, given that the population is  $2000$  at  $t=0.$

(b)   Use your answer to part (a) to find the size of the population after one month.

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Solution

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