Answer:
To write an exponential regression equation for this set of data, we can use the formula y = ab^x, where y is the value of the car in dollars, x is the number of years since purchase, a is the initial value of the car, and b is the rate of depreciation.
To find the values of a and b, we can use the first two data points:
y = ab^x
14220 = ab^1
Solving for a, we get:
a = 14220 / b
Now, we can substitute this expression for a into the first data point:
y = ab^x
15700 = (14220 / b) * b^0
Simplifying, we get:
15700 = 14220
This is not a valid equation, so we need to adjust our estimate for the rate of depreciation, b. One way to do this is to take the average of the depreciation rates between each pair of consecutive data points:
b = (14220/15700)^(1/6)
b = 0.9497
Now, we can use this value of b to find the value of a:
a = 14220 / b
a = 14955.15
Therefore, the exponential regression equation for this set of data is:
y = 14955.15 * 0.9497^x
To find the value of the car after 9 years, we can substitute x = 9 into the equation:
y = 14955.15 * 0.9497^9
y = 7327.78
Therefore, the value of the car, to the nearest cent, after 9 years is $7327.78.