A savings account advertises an annual percentage yield (APY) of 5.4%, which means that the balance in the account increases at an annual growth rate of 5.4%/yr.

a. Find the balance in the account for t ≥ 0 with an initial deposit of $1500, assuming the APY remains fixed and no additional deposits or withdrawals are made.

b. What is the doubling time of the balance?

c. After how many years does the balance reach $5000?