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.
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.