Set 5: Exponential Functions (Intermediate)

Choice A is correct. Choice A is the correct answer. Solve for when $y = 9$. 1. Set Equal: $6(1.5)^x = 9$. 2. Divide: $(1.5)^x = \frac{9}{6} = 1.5$. 3. Recognize: $(1.5)^x = 1.5^1$, so $x = 1$. 4. Point: $(1, 9)$. Strategic Tip: When the result equals the base, $x = 1$. Choice B is incorrect because at $x=2$, $y = 6(1.5)^2 = 13.5 \neq 9$. Choice C is incorrect because this would give an even larger $y$ value. Choice D is incorrect because at $x=0$, $y = 6$, not 9.