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**Kakariki** Hey, I have a word problem here, and I am asking to ensure that I am finding the correct thing.

**Question:** The amount of pollution in a certain lake is $\displaystyle P(t) = (t^{1/4} + 3)^3 $, where t is measured in years, and P is measured in parts permillion (ppm). At what rate is the amount of pollution changing after 16 years?

**Answer: **I am understanding this to be asking me what the instantaneous rate of change is at the 16 year mark. So I find the derivative of $\displaystyle P(t) = (t^{1/4} + 3)^3 $ which is $\displaystyle \frac {3(t^{1/4} + 3)^2}{4(t^{3/4})} $. Then I plug t = 16 into this derivative and this is my answer.

Am I doing the what the question asks?