The car will be worth $5026.21 after 11 years.
To find an exponential regression equation for the data in the table, we can use the following steps:
1. Enter the data into a calculator or spreadsheet program.
2. Select the exponential regression function.
3. Calculate the regression coefficients.
4. Round the regression coefficients to the nearest thousandth.
The following table shows the results of these steps:
| Coefficient | Value |
| a | 14000 |
| b | 0.911 |
Therefore, the exponential regression equation for the data is:
y = 14000 * 0.911^x
To determine the value of the car after 11 years, we can simply substitute 11 for x in the equation:
y = 14000 * 0.911^11
y = 5026.21
Therefore, the value of the car after 11 years is **$5026.21**.
In addition to the above, here is a brief explanation of exponential regression:
Exponential regression is a type of regression analysis that is used to model data that changes at a rate that is proportional to its current value.
The general form of an exponential regression equation is:
y = a * b^x
where:
y is the dependent variable (the value we are trying to predict)
x is the independent variable (the value we are using to predict y)
a and b are the regression coefficients
The coefficient a represents the initial value of y, and the coefficient b represents the growth rate of y.
If b is greater than 1, then y is increasing exponentially.
If b is less than 1, then y is decreasing exponentially.
If b is equal to 1, then y is constant.
Exponential regression is a powerful tool that can be used to model a wide variety of data, including population growth, economic growth, and the spread of disease.