Question

the table gives the amount of debt, in dollars, on an individuals credit card for certain months after opening the credit card. using an exponential regression ( y = ab^{x} ) to model these data, what is the debt at month 24 predicted by the exponential function model, to the nearest dollar? (assume that the debt continues and that no payments are made to reduce the debt.)

Explanation:

Step1: Input data into calculator

Using a graphing calculator, input the data points \((1,620)\), \((4,1083)\), \((5,1215)\), \((7,1902)\) into the exponential regression function.

Step2: Obtain regression equation

After running the exponential regression (\(y = ab^{x}\)), we get \(a\approx450\) and \(b\approx1.2\). So the equation is \(y = 450\times(1.2)^{x}\).

Step3: Substitute \(x = 24\)

Substitute \(x = 24\) into the equation \(y=450\times(1.2)^{24}\).

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Answer:

C. \(42,159\)