Suppose that $30,000 is invested at 8% interest, compounded annually. After time t, in years, it grows to the amount. A given by the function A(t)=$30,000(1.08)^t

a) Find the amount of time after which there will be $90,000 in the account.

=> 90000 = 30000(1.08)^t

=> 1.08^t = 3

=> t = ln3/ln1.08

=> t = 14.27 years

b) Find the doubling time.

=> (1.08)^t = 2

=> t = ln(2)/ln(1.08)

=> t = 9 years