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

`y=13700(0.919)^x`

Value of the car after 12 year: $4971.72

Step-by-step 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=(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`