Set 17: Exponential Functions (Advanced)

Choice A is correct. Choice A is the correct answer. Find $a$ and $b$ from the points. 1. Point 1: $12= a(b)^1 = ab$. 2. Point 2: $108= a(b)^3 = ab^3$. 3. Divide: $\frac{108}{12} = b^2 = 9$, so $b = 3$. 4. Find $a$: $a(3) = 12$, so $a = 4$. 5. Verify: $4(3)^1 = 12$ ✓, $4(3)^3 = 108$ ✓ Strategic Tip: Divide equations to eliminate $a$ and solve for $b$ first. Choice B is incorrect because at $x=1$, this gives $12(3)=36 \neq 12$. Choice C is incorrect because the base and coefficient are swapped. Choice D is incorrect because both values are from points, not the equation.