Question

A bacteria population is 2000 at time t = 0 and its rate of growth is 1000 · 5t bacteria per hour after t hours. what is the population after one hour? (round your answer to the nearest whole number.)

Answer 1

Since you are given the rate of growth, the population must be computed from the integral ...

$\displaystyle p(t)=2000+\int_{0}^{t}{\left(1000\cdot 5^{t}\right)}\,dt=2000+\frac{1000}{\ln{(5)}}\cdot \left(5^{t}-1\right)\\\\=2000+\frac{1000}{\ln{(5)}}\cdot 4\approx 4485\qquad\mbox{after 1 hour}$