population of flies rate of change (quick q)?

Question

nasty stuff, lol

a population of flies is growing in a large box. the number of flies P (in hundreds) after t weeks is given by P(t)= 12t^2 - t^4 + 5

c. find P'(t) (think this means the derivative)

d. when does the population stop growing?

Answer 1

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Yes, P'(t) is the derivative with respect to t. I suppose you know how to do this, just take the derivative of each of the 3 terms and add them up. The derivative of 5 is just 0, because it doesn't change with respect to t.

Once you get P'(t), this is the rate of population growth.

Set P'(t)=0 and solve for t.

Presumably that is when the population stops growing (because that is when the rate of change of P is 0). You might want to check to make sure the population actually stops growing for higher values of t.