1. **Problem statement:** We need to find an exponential depreciation model of the form $$V(t) = V(0) e^{-rt}$$ where $V(t)$ is the value at time $t$, $V(0)$ is the initial value, and $r$ is the depreciation rate. 2. **Formula explanation:** The formula $$V(t) = V(0) e^{-rt}$$ represents exponential decay, where the value decreases continuously at a rate proportional to its current value. 3. **Important rules:** - $V(0)$ is the initial value at time $t=0$. - $r > 0$ is the decay constant (rate of depreciation). - As $t$ increases, $V(t)$ decreases exponentially. 4. **Finding the model:** To find the model, you need the initial value $V(0)$ and the depreciation rate $r$. If you have data points, you can solve for $r$ by using values of $V(t)$ at a known time $t$: $$V(t) = V(0) e^{-rt} \implies e^{-rt} = \frac{V(t)}{V(0)} \implies -rt = \ln\left(\frac{V(t)}{V(0)}\right) \implies r = -\frac{1}{t} \ln\left(\frac{V(t)}{V(0)}\right)$$ 5. **Summary:** The exponential depreciation model is $$V(t) = V(0) e^{-rt}$$ where $r$ can be calculated if you know the initial and later values. This is the general form of the exponential depreciation model.