A culture of cells has an initial population of 200 at \(t=0\). The growth rate of the cells is given by
\[ P'(t) = 60e^{-0.2t} \]
where \(P'(t)\) is measured in cells per hour.
The number of cells after 2 hours (rounded to the nearest cell) is
\[ P(2) = \answer {299} \]
For \(t\geq 0\) the number of cells is given by
\[ P(t) = \answer {500 - 300e^{-0.2t}}. \]
The limiting population of the culture is
\[ \lim _{n\to \infty } P(t) = \answer {500}. \]
We see then that the culture grows without boundlevels off at a finite, nonzero populationdies off in the long run.