1. **Problem statement:** A sports car worth 20000 decreases in value by 15% each year. 2. **Modeling the depreciation:** The value after $t$ years is given by the formula for exponential decay: $$V = V_0 (1 - r)^t$$ where $V_0 = 20000$ is the initial value and $r = 0.15$ is the rate of decrease. 3. **Writing the equation:** Substituting values: $$V = 20000 (0.85)^t$$ 4. **Calculating the value after 8 years:** Substitute $t=8$: $$V = 20000 (0.85)^8$$ 5. **Intermediate calculation:** $$0.85^8 \approx 0.27249$$ 6. **Final value:** $$V \approx 20000 \times 0.27249 = 5449.8$$ --- 1. **Problem statement:** Sketch the graph of $y = 8 \left(\frac{1}{2}\right)^x$ and find coordinates of the y-intercept and two other points. 2. **Y-intercept:** At $x=0$: $$y = 8 \left(\frac{1}{2}\right)^0 = 8 \times 1 = 8$$ 3. **Other points:** - At $x=1$: $$y = 8 \times \frac{1}{2} = 4$$ - At $x=2$: $$y = 8 \times \left(\frac{1}{2}\right)^2 = 8 \times \frac{1}{4} = 2$$ --- 1. **Problem statement:** Evaluate expressions leaving answers in fraction form. 2. **a) Evaluate $4^{-2}$:** $$4^{-2} = \frac{1}{4^2} = \frac{1}{16}$$ 3. **b) Evaluate $\sqrt[3]{\frac{1}{64}}$:** Since $64 = 4^3$, $$\sqrt[3]{\frac{1}{64}} = \frac{1}{\sqrt[3]{64}} = \frac{1}{4}$$