Solve the Problem $v=46,300+100 t^{2}$ , 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 $v=46,300+100 t^{2}$ , 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. The graph has an absolute maximum at $(0,46,300)$ , and a local maximum at one other point. What is the value of $t$ at the local maximum? What is the discounted value of the collection at that time?

A) $t=38$ ; at which time the discounted value is $\$ 41,555.26$ .
B) $t=38.34$ ; at which time the discounted value is $\$ 41,359.76$ .
C) $\mathrm{t}=37.73$ ; at which time the discounted value is $\$ 41,709.19$ .
D) $t=39.59$ ; at which time the discounted value is $\$ 40,623.55$ .