1. **State the problem:** We need to find a linear depreciation model for the value of a car over time, given its initial value and current value after 3 years. 2. **Formula:** The linear depreciation model is given by $$V(t) = mt + b$$ where: - $V(t)$ is the value of the car at time $t$ years, - $m$ is the rate of depreciation per year (slope), - $b$ is the initial value of the car (intercept). 3. **Identify known values:** - Initial value at $t=0$: $V(0) = 45000$ - Value after 3 years: $V(3) = 25000$ 4. **Find the slope $m$:** The slope $m$ is the change in value over change in time: $$m = \frac{V(3) - V(0)}{3 - 0} = \frac{25000 - 45000}{3} = \frac{-20000}{3} = -6666.67$$ 5. **Find the intercept $b$:** Since $b$ is the initial value at $t=0$, we have: $$b = 45000$$ 6. **Write the linear model:** $$V(t) = -6666.67t + 45000$$ This model shows the car loses approximately 6666.67 units of value each year.