Solve the Problem $v=45,600+100 t^{2}$ , 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 $v=45,600+100 t^{2}$ , 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. What is the value of $t$ at the absolute maximum? What is the discounted value of the collection at that time?

A) $\mathrm{t}=0$ ; at which time the discounted value is $\$ 45,600$ .
B) $\mathrm{t}=12.63$ ; at which time the discounted value is $\$ 47,592.54$ .
C) $t=36.23$ ; at which time the discounted value is $\$ 49,612.90$ .
D) $t=38.45$ ; at which time the discounted value is $\$ 46,734.12$ .