You have a $10,000 balance on your credit card. The card has a 14% annual interest rate, which is compounded monthly. The minimum payment each month is 2.5% of the balance. For simplicity, assume:

No new purchases, charges, or fees are applied to the credit card.

Interest is calculated based on the balance at the end of the month.

Interest and payments are applied to the account simultaneously on the last day of each month. I.e. if your balance is x dollars, they will add the interest based on x dollars (disregarding your payment), and you will pay the minimum amount based on x dollars as well (disregarding the interest that got charged).

Suppose you have decided to pay only the minimum payment (2.5%) each month.

1. Write an exponential function f(t) that will give your balance after t months.

2. How long will it take before your balance is less than $1000 ? Be sure to specify units