Set 14: Exponential Functions (Advanced)

Choice A is correct. Choice A is the correct answer. Find the half-life. 1. Target: Half of 5000 = 2500. 2. Equation: $2500= 5000(0.92)^t$, so $(0.92)^t = 0.5$. 3. Test: - $t=8$: $(0.92)^8 \approx 0.513$ (close to 0.5) ✓ - $t=9$: $(0.92)^9 \approx 0.472$ (below 0.5) 4. Answer: About 8 years. Strategic Tip: For decay factor 0.92, half-life ≈ $\frac{\ln(0.5)}{\ln(0.92)} \approx 8.3$ years. Choice B is incorrect because decay is faster. Choice C is incorrect because $(0.92)^4 \approx 0.716 \neq 0.5$. Choice D is incorrect because $(0.92)^6 \approx 0.606 \neq 0.5$.