1. ## Population Growth.... Help Please!

A certain species of virulent bacteria is being grown in a culture. It is observed that the rate of growth of the bacterial population is proportional to the number present. If there were 4000 bacteria in the initial population and the number doubled after the first 60 minutes, how many bacteria will be present after 3 hours?

I was confused when it said "the bacterial population is proportional to the number present." How would that be written?

2. Originally Posted by runner07
A certain species of virulent bacteria is being grown in a culture. It is observed that the rate of growth of the bacterial population is proportional to the number present. If there were 4000 bacteria in the initial population and the number doubled after the first 60 minutes, how many bacteria will be present after 3 hours?

I was confused when it said "the bacterial population is proportional to the number present." How would that be written?
Call the population size at time t N(t). Then the rate of growth of the population at time t will be $\displaystyle \frac{dN}{dt}$. The proportionality statement says:
$\displaystyle \frac{dN}{dt} \propto N(t)$

-Dan