Posted by **Nick** on Saturday, March 5, 2011 at 10:42pm.

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?

- calculus -
**bobpursley**, Saturday, March 5, 2011 at 10:52pm
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

- calculus -
**Nick**, Saturday, March 5, 2011 at 10:54pm
That's what I have done, I have expanded it to get the derivative, but I am having problems solving for t.

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