Question

If the fish population, p, in a lake can be modelled by the function p(t)=15(t^2+30)(t+8), where t is the time, in years , from now.

How do I determine the rate of change when the population when there are 5000 fish in the lake?

Answer 1

You take the derivative of p

expand p
p=15(t^3+240+30t+8t^2)
p'=15(3t^2+30+16t)

in the first equation,p=5000, so you have to solve for t. A little algebra is required. Then, for the real t, put that in the p' equation

Answer 2

That's what I have done, I have expanded it to get the derivative, but I am having problems solving for t.