Question

The accompanying table shows the value of a car over time that was purchased for 17000 dollars , where x is years and y is the value of the car in dollars . Write an exponential regression equation for this set of data, rounding all coefficients to the nearest thousandth . Using this equation , determine the value of the car , to the nearest cent , after 8 years .

Answer 1

Using Microsoft Excel, the data set is plotted and the resulting plot is shown below with its corresponding exponential regression equation

Since the problem wants that the coefficient for the exponential regression equation is on the nearest thousandth, the exponential regression equation will be

`y=17,189.973e^(-0.115x)`

We use this equation to solve for the value of the car after 8 years. At x = 8, we get

`y=17,189.973e^{-0.115(8)_{}}=6850.53`