v(t)= Ce^(k(square root(t))

Question

Suppose that the dealer, who is 25 years old, decides to sell the card at time , sometime in the next 40 years: 0< or equal to t < or equal to 40. At that time , he’ll invest the money he gets for the sale of the card in a bank account that earns an interest rate of r , compounded continuously. (This means that after years, an initial investment of will be worth Ie^(rt).) When he turns 65, he’ll take the money that’s in his bank account and begin to draw on it for his retirement. Let A be the amount of money in his account when he turns 65.

4. Write an expression for A(t), the amount of money in the dealer’s account when he turns 65 written as a function of t , the time at which he sells the baseball card.

Answer 1

money from card sale at time t:
v(t) = Ce√(kt)
time left to draw interest: 40-t
A = Ce√(kt) * e^(r(40-t))
= Ce^(√(kt)+r(40-t))