Originally Posted by

**Macleef** **It is projected that, t, years from now, the population of a certain country will become $\displaystyle P(t) = 50e^{0.002t}$ million.**

**a) At what rate will the population be changing with respect to time 10 years from now?**

...I thought taking the first derivative of the equation would give me the rate of change... and it did... but it's not the answer the question is looking for.

$\displaystyle P'(t) = e^{0.02t}$

...and I solved for 10 years and compared the population to the present...

$\displaystyle P(10) = 61$ million

$\displaystyle P(0) = 50$ million

$\displaystyle P(10) - P(0) = 11$ million

rate of change $\displaystyle = \frac{P(10) - P(0)}{10 - 0}$

rate of change $\displaystyle = 1.1$

...and that's also not the right answer...

So... now I don't know what to do.