You Manage a Small Antique Store That Owns a Collection $v = \frac { 12,000 } { 1 + 500 e ^ { - 0.5 t } }$

You manage a small antique store that owns a collection of Louis XVI jewelry boxes. Their value v is increasing according to the formula $v = \frac { 12,000 } { 1 + 500 e ^ { - 0.5 t } }$
Where t is the number of years from now. You anticipate an inflation rate of 1% per year, so that the present value of an item that will be worth $v in t years' time is given by
$p = v ( 1.01 ) ^ { - t }$
In how many years from now will the greatest rate of increase of the present value of your antiques be attained Round your answer to two decimal places.

A) t = 24.55 years
B) t = 3.07 years
C) t = 11.27 years
D) t = 12.27 years
E) t = 6.14 years