Set 5: Exponential Functions (Advanced)

Choice A is correct. Choice A is the correct answer. Find when height reaches 15 feet. 1. Formula: $H(t) = 10(1.08)^t$, solve for $15= 10(1.08)^t$. 2. Simplify: $(1.08)^t = 1.5$. 3. Test: - $t=5$: $(1.08)^5 \approx 1.469$ (below 1.5) - $t=6$: $(1.08)^6 \approx 1.587$ (above 1.5) 4. Answer: Between 5 and 6 years. Strategic Tip: Test consecutive integer values to bracket the answer. Choice B is incorrect because growth happens much faster. Choice C is incorrect because $(1.08)^3 \approx 1.26 < 1.5$. Choice D is incorrect because it reaches 15 feet before year 8.