N this activity, you will formulate and solve an exponential equation that models a real-world situation. Emma doesn’t have experience using credit cards. In fact, she just got her first one. She is also about to start her first year of college. She uses her new credit card to purchase textbooks for her classes. The total comes to $300. These are the terms of her credit card:

It has a 15% annual interest rate.
The interest is compounded monthly.
The card has $0 minimum payments for the first four years it is active.
The expression that models this situation is , where P represents the initial, or principal, balance; r represents the interest rate; t represents the time in years; and n represents the number of times the interest is compounded per year.

Identify the values of P, r, and n in the expression based on Emma’s situation. Then substitute those values into the formula to write a simplified exponential expression in terms of time.

Replace the variables a, b, and c to write the expression