Suppose your family owns a rare book whose value t years from now will be $V ( t ) = 7 e ^ { \sqrt { 0.6 t } }$ 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) 34.72 years
B) 41.67 years
C) 111.11 years
D) 180.56 years

Question

Quizplus · Accepted Answer

The optimal time to sell is when the rate of increase in the book's value equals the interest rate. Solving $ \frac{dV}{dt} = 0.06V(t) $ gives approximately 41.67 years.

Suppose Your Family Owns a Rare Book Whose Value T V(t)=7e0.6tV ( t ) = 7 e ^ { \sqrt { 0.6 t } }V(t)=7e0.6t​

Suppose Your Family Owns a Rare Book Whose Value T $V ( t ) = 7 e ^ { \sqrt { 0.6 t } }$