1. **State the problem:** We have a vehicle whose value $D$ in dollars depreciates over time $t$ in years according to a function (not explicitly given in the prompt). We want to find the time $t$ when the vehicle's value is $20,000$. 2. **Assume the depreciation function:** Typically, vehicle depreciation can be modeled by an exponential decay function such as $$D(t) = D_0 e^{-kt}$$ where $D_0$ is the initial value and $k$ is the depreciation rate. 3. **Set up the equation:** We want to find $t$ such that $$D(t) = 20000$$ 4. **Solve for $t$:** $$20000 = D_0 e^{-kt}$$ Divide both sides by $D_0$: $$\frac{20000}{D_0} = e^{-kt}$$ Take the natural logarithm of both sides: $$\ln\left(\frac{20000}{D_0}\right) = -kt$$ Solve for $t$: $$t = -\frac{1}{k} \ln\left(\frac{20000}{D_0}\right)$$ 5. **Interpretation:** To find the exact time, you need the initial value $D_0$ and the depreciation rate $k$. Once you have those, plug them into the formula above to get $t$. **Final answer:** $$t = -\frac{1}{k} \ln\left(\frac{20000}{D_0}\right)$$