Thread: Population growth

Here is my problem:

"A bacteria culture grows with the constant relative growth rate. After 2 hours there are 600 bacteria and after 800 hours the count is 75,000.

Find the initial population."

I know I need to use P(t)=P(0)(e^kt) but can't figure out how to solve for P(0). I'm sure it is probably obvious, but I am stumped. Any help is appreciated.

You are given two data points, (t, P) = (2, 600) and (t, P) = (800, 75000). Plug these values in, and solve the resulting system of equations for the values of P0 and k.

That's what I did first, but I got 0.0060505 for K, which seemed like it couldn't be right. I guess my prof just wanted to give us crappy numbers to work with :/ Thanks.