A seller on ebay has a rare basketball, which was used in the 2012 London Olympics and was signed by the basketball giant, Kobe Bryant. The seller is trying to decide when to sell it, and he is asking for 980 USD at this stage. He knows its value will grow over time, but he could sell it and invest the money in a bank account, and the value of the money would also grow over time due to interest. The question is: when should the seller sell the basketball? Experience suggests to the seller that over time, the value of the basketball, like many other collectibles, will grow in a way consistent with the following model: V(t)=Ae^(sqrt(t)). Where A and are constants, and V(t) is the value of the basketball in dollars at time t years after the present time.
Let t0 be the optimal time to sell the basketball, i.e., the time that will maximize M(t). Try to find in the general model. Note that your solution should be a function of the constant variables A, , and r.
