1. **State the problem:** We are given the value of a car over time and need to find an exponential regression equation of the form $$y = ab^x$$ where $y$ is the value of the car after $x$ years. 2. **Given data:** $$\begin{array}{c|c} \text{Years }(x) & \text{Value }(y) \\ \hline 0 & 15500 \\ 1 & 13737 \\ 2 & 11176 \\ 3 & 10460 \\ 4 & 8203 \end{array}$$ 3. **Find $a$:** Since $x=0$ corresponds to the initial value, $$a = y(0) = 15500$$ 4. **Find $b$:** Use another point, for example $x=1$, $y=13737$: $$13737 = 15500 \times b^1$$ Divide both sides by 15500: $$\frac{13737}{15500} = \cancel{\frac{15500}{15500}} b$$ $$b = 0.886$$ (rounded to three decimals) 5. **Exponential regression equation:** $$y = 15500 \times 0.886^x$$ 6. **Find value after 8 years:** $$y(8) = 15500 \times 0.886^8$$ Calculate the power: $$0.886^8 \approx 0.382$$ Multiply: $$y(8) = 15500 \times 0.382 = 5911.00$$ **Final answer:** The value of the car after 8 years is approximately $5911.00$ dollars.