Question

Jacki plans to pay for the down payment of a new car with her credit card. The annual interest rate for her credit card is 17%. The following expression represents the balance of the credit card, in dollars, after t years. 2,250(1.17)^t

Write an exponential expression in the form (b)c that reveals the monthly interest rate of Jacki's credit card. Round any decimals to the nearest thousandth.

Answer 1

`A=2250(1.014)^(12t)` is the exponential expression.

Explanation:

The expression which represents the balance of credit card, in dollars, after t years is

`A=2250(1+(0.17)/(12))^(12t)`

Where rate of interest is 17% and amount spent is $2250.

Since 17% interest is the annual interest and we have done the expression in the form of monthly compounding.

So the expression will be

`A=A_(0)[1+.014]^(12t)`

`A=A_(0)(1.014)^(12t)`

`A=2250(1.014)^(12t)`

Answer 2

Given that the annual interest rate of Jacki's credit card is 17%, then the exponential expression that reveals the monthly interest rate of Jacki's credit card is given by:


`2,250\left(1+(0.17)/(12)\right)^(12t)=2,250(1+0.014)^(12t) \\ \\ =\bold{2,250(1.014)^(12t)}`