Set 16: Exponential Functions (Advanced)

Choice A is correct. Choice A is the correct answer. Find when value doubles. 1. Formula: $V(t) = 0.50(1.15)^t$, solve for $1.00= 0.50(1.15)^t$. 2. Simplify: $(1.15)^t = 2$. 3. Test: - $t=4$: $(1.15)^4 \approx 1.749$ (below 2) - $t=5$: $(1.15)^5 \approx 2.011$ (above 2) ✓ 4. Answer: Between 4 and 5 weeks. Strategic Tip: Rule of 72 gives rough estimate: $\frac{72}{15} \approx 4.8$ weeks. Choice B is incorrect because doubling happens sooner. Choice C is incorrect because growth is much faster. Choice D is incorrect because $(1.15)^2 \approx 1.32 \neq 2$.