Exponential Equation Word Problem - Credit Card Interest Rate

Question

The exponential function describing the balance owec on Jasmin's credit card, B, t years after she purchases a TV on that credit card for $480 is

B(t)=480*(1.15)^t

According to this equation, what is the interest rate for this credit card (in %)?

Use this function (and logs) to compute how long it takes (in years) until the balance on Jasmin's credit card is $1700.

Find the exact log expression and a decimal rounded to the nearest thousandth.

Answer 1

Hey Joshua! An interest rate is money added onto your bill every year as a fee for borrowing the banks money! So lets say there was absolutely no interest! Then you would expect that the amount she owes would not change. In this case, the equation would be

B(t) = 480 * (1.00)^t

Based on this equation, she would always owe $480. In this problem, however, there is interest! Every year, the price goes up. When you include an interest rate, the equation looks like

B(t) = 480 * (1.00 + r) ^t

Here, r is the interest rate, and is the amount added onto that interest free equation. So in this particular problem, what do you think the interest is?

The second part is solving. Here, we know B(t), or the balance on her credit card and need to find what t is

1700 = 480 * (1.15) ^t ----> 1700 / 480 = 1.15^t

One rule of logs say that if you take the log of each side of the equation, the exponent can be brought in front like so

Log(1700/480) = t * log(1.15)

Once you utilize this log rule, the algebra becomes much easier!