Suppose your family owns a rare book whose value t years from now will be $V ( t ) = 9 e ^ { \sqrt { 0.8 t } }$ dollars.If the prevailing interest rate remains constant at 6% per year compounded continuously,when will it be most advantageous for your family to sell the book and invest the proceeds? Round your answer to two decimal places.
A)125.00 years
B)48.61 years
C)194.44 years
D)55.56 years

Question

Quizplus · Accepted Answer

To find when to sell the book, we need to maximize the present value of the book, which is given by $V(t) \times e^{-0.06t}$. Differentiating and setting the derivative to zero gives the optimal time to sell as approximately 55.56 years.

Suppose Your Family Owns a Rare Book Whose Value T V(t)=9e0.8tV ( t ) = 9 e ^ { \sqrt { 0.8 t } }V(t)=9e0.8t​

Suppose Your Family Owns a Rare Book Whose Value T $V ( t ) = 9 e ^ { \sqrt { 0.8 t } }$