Solve the Problem $v=44,700+100 t^{2}$ , Where $t$ Is the Number of Years from Now

Multiple Choice

Solve the problem.
-It is estimated that the total value of a stamp collection is given by the formula $v=44,700+100 t^{2}$ , where $t$ is the number of years from now. If the inflation rate is running continuously at $4 \%$ per year so that the (discounted) present value of an item that will be worth $\$ v$ in $t$ years' time is given by $\mathrm{p}=\mathrm{ve}^{-.04 \mathrm{t}}$ . Sketch the graph of the discounted value as a function of time at which the stamp collection is sold. At what value of $t$ is the present value increasing most rapidly?

A) $t=19.66$
B) $t=24.76$
C) $t=19.36$
D) $t=21.66$