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

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. The graph has one local minimum. What is the value of $t$ at the local minimum? What is the discounted value of the collection at that time?

A) $t=12$ ; at which time the discounted value is $\$ 37,404.36$ .
B) $\mathrm{t}=10.41$ ; at which time the discounted value is $\$ 36,313.93$ .
C) $\mathrm{t}=12.27$ ; at which time the discounted value is $\$ 35,436.18$ .
D) $t=11.66$ ; at which time the discounted value is $\$ 36,566.26$ .