My friend had to do this problem in Calculus BC. I'm no good at calculus, but I decided it was be fun for someone to figure it out for me. A bacteria culture starts with 500 bacteria and grows at a rate proportional to its size. After 3 hours there are 8000 bacteria. (a) Find an expression for the number of bacteria after t hours. (b) Find the number of bacteria after 4 hours. (c) Find the rate of growth after 4 hours. (d) When will the population reach 30,000? I think it involves differential equations.
Yeah that amused me too .I'd probably start a little earlier: Growth proportional to size implies..... [tex]\frac{dy}{dt}=ky[/tex] with the intial condition [tex]y(0)=500[/tex] and the time t = 3 (in hours!) condition [tex]y(3)=8000[/tex]. Your mission, should you choose to accept it, is to find the general solution to the DE above, and the values of k and the constant of integration A. That's the model, the rest should be ok?