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

very interesting

the equation we are given is for when the units of t are in years

I do know that you want to have the variable as time, but I'm not sure if you want it in years or months

I will solve for in months because that makes more sense

in that case, it will be 2250(1+r)^m where r=monthly interest rate and m=time in months

to compare, we can do

when 1 year has elapsed, t=1 and m=12

and the amount earned should be the same

so therfor we can say

$2250(1.17)^1=2250(1+r)^{12}$

divide both sides by 2250 to make it easier

$1.17^1=(1+r)^{12}$

$1.17=(1+r)^{12}$

take 12th root of both sides

$\sqrt[12]{1.17}=1+r$

minus 1 both sides

$-1+\sqrt[12]{1.17}=r$

using a calculator

-1+1.01316961=r

0.01316961=r

not sure if yu want percent to thousandth or decimal to thousandth

if decimal then 0.013 is interest rate

if percent then it is 1.317% interest rate