The question is:

If a rare antique appreciates over time according to f(t) = K (e^(t^0.5)) and the interest rate is r;
1) What would be the present value (PV) of selling it at time t?
2) What time of sale would maximise this present value?

For question 1, I used (e^(-rt)) so that PV = K(e^((t^o.5) - rt))

As for part two I have thought about several things such as taking natural logs of both sides first and differentiating twice and then making that equal to zero, but can't quite seem to make it work.

Ideas?

Thanks for anyone who can help me out in any way and sorry for the large use of bracketing but I wanted to make sure you guys (and gals) knew which parts where being raised to the power of which other parts.

Thanks again!