1. **Problem Statement:** We are given the function $$V(t) = 2000 \left(\frac{1}{2}\right)^{\frac{t}{h}}$$ which models exponential decay with an initial value of 2000 and a half-life of $h$ years. 2. **Formula Explanation:** This is an exponential decay function where: - $2000$ is the initial amount at time $t=0$. - $\left(\frac{1}{2}\right)^{\frac{t}{h}}$ represents the decay factor, halving the quantity every $h$ years. 3. **Key Rules:** - When $t = 0$, $V(0) = 2000$. - When $t = h$, $V(h) = 2000 \times \frac{1}{2} = 1000$. - The function decreases by half every $h$ years. 4. **Intermediate Work:** - To find the value at any time $t$, substitute $t$ into the formula. - For example, at $t = 2h$, $$V(2h) = 2000 \left(\frac{1}{2}\right)^{\frac{2h}{h}} = 2000 \left(\frac{1}{2}\right)^2 = 2000 \times \frac{1}{4} = 500.$$ 5. **Interpretation:** This function models how a quantity decreases over time by half every $h$ years, which is typical in radioactive decay or similar processes. **Final answer:** The function $$V(t) = 2000 \left(\frac{1}{2}\right)^{\frac{t}{h}}$$ correctly models exponential decay with half-life $h$ and initial value 2000.