Question

Creating an Exponential Model

In 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 P(1 + r/n)^nt, where (1 + r/n) represents the growth factor of the interest rate.

Answer 1

P = $300

r = 0.15

n = 12

$544.61 (to the nearest cent)

`P(1+r)^t`

$524.70 (to the nearest cent)

Explanation:

P = principal amount = $300

r = annual interest rate in decimal form = 15% = 15/100 = 0.15

n = number of times interest is compounded per unit t = 12

How much she'll owe in 4 years

P = 300

r = 0.15

n = 12

t = 4

`P(1+(r)/(n))^(nt)=300(1+(0.15)/(12))^(12 * 4)`

= $544.61 (to the nearest cent)

Yearly compounding interest rate

`P(1+r)^t`

How much she'll owe in 4 years at yearly compounding interest

`P(1+r)^t=300(1+0.15)^4`

= $524.70 (to the nearest cent)