# 007B Sample Midterm 1, Problem 2

${\displaystyle P'(t)=500e^{-t}}$
where  ${\displaystyle P(t)}$  is the population after  ${\displaystyle t}$  months.
(a)   Find a formula for the population size after  ${\displaystyle t}$  months, given that the population is  ${\displaystyle 2000}$  at  ${\displaystyle t=0.}$