Question

The accompanying table shows the value of a car over time that was purchased for 13700 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 12 years ,

Answer 1

ANSWER

$y=13700(0.919)^x$

Value of the car after 12 year: $4971.72

EXPLANATION

The exponential regression equation is

$y=ab^x$

Using the values of the table we can find both a and b. Note that a is the value of y when x = 0, so a = 13700.

For b replace a, and x and y with the next values of the table:

$\begin{gathered} 12590=13700b^1 \\ b=\frac{12590}{13700} \\ b\approx0.919 \end{gathered}$

The equation is

$y=13700(0.919)^x$

To find the value of the car after 12 years, replace x = 12:

$y=13700(0.919)^{12}\approx4971.72$