1. **Problem Statement:** A company buys cars for 28000 each and depreciates them straight-line over 7 years, losing 4000 in value each year. We need to: (a) Write a linear function for book value $V$ as a function of age $x$. (b) Sketch the function. (c) Find the book value after 3 years and interpret the slope. (d) Find when the book value will be 8000. 2. **Formula and Explanation:** Straight-line depreciation means the value decreases by a fixed amount each year. The function is linear: $$V(x) = \text{initial value} - (\text{depreciation per year}) \times x$$ Here, initial value is 28000 and depreciation per year is 4000. 3. **Part (a): Write the function** $$V(x) = 28000 - 4000x$$ where $x$ is the age in years and $V(x)$ is the book value. 4. **Part (b): Sketch the function** The function is a line starting at $V(0) = 28000$ and decreasing by 4000 each year until $V(7) = 0$. 5. **Part (c): Book value after 3 years** Calculate: $$V(3) = 28000 - 4000 \times 3 = 28000 - 12000 = 16000$$ Interpretation: The slope $-4000$ means the car loses 4000 in value every year. 6. **Part (d): When is book value 8000?** Set $V(x) = 8000$: $$8000 = 28000 - 4000x$$ Solve for $x$: $$4000x = 28000 - 8000 = 20000$$ $$x = \frac{20000}{4000} = 5$$ So, after 5 years, the book value will be 8000. **Final answers:** (a) $V(x) = 28000 - 4000x$ (c) $V(3) = 16000$ (d) $x = 5$ years