# 007A Sample Midterm 3, Problem 2

Suppose the size of a population at time  ${\displaystyle t}$  is given by
${\displaystyle N(t)={\frac {1000t}{5+t}},~t\geq 0.}$
(a) Determine the size of the population as  ${\displaystyle t\rightarrow \infty .}$  We call this the limiting population size.
(b) Show that at time  ${\displaystyle t=5,}$  the size of the population is half its limiting size.