A new company is growing so that its value t years from now will be 50t^2 dollars. Therefore, its present value (at the rate of 8% compounded continuously) is
V(t) = (50t^2)(e^-0.08t) dollars (for t 0)
Find the number of years that maximizes the present value. Verify answer.

Question

A new company is growing so that its value t years from now will be 50t^2 dollars.  Therefore, its present value (at the rate of 8% compounded continuously) is 
V(t) = (50t^2)(e^-0.08t) dollars (for t >0)
Find the number of years that maximizes the present value. Verify answer.

dumbcow · Answer

set derivative equal to 0.....use product rule
$$V'(t) = 100t(e^{-.08t}) + 50t^{2}(-.08)e^{-.08t} = 0$$

anonymous · Answer

ok. Thank you.

anonymous · Answer

What is the next step to solve this problem?

dumbcow · Answer

factor out the e^-.08t
solve resulting quadratic for "t"

dumbcow · Answer

notice
$$e^{-.08t} = 0$$
has no solution

anonymous · Answer

so at this point the problem would look like..
(e^-0.08t) (100t+(50t^2)(-0.08)) ?