Set 12: Exponential Functions

Choice A is correct. Choice A is the correct answer. Use the two points to find $a$ and $b$. 1. Point 1: $6= a(b)^1 = ab$. 2. Point 2: $54= a(b)^3 = ab^3$. 3. Divide: $\frac{54}{6} = \frac{ab^3}{ab} = b^2 = 9$, so $b = 3$. 4. Find $a$: $a(3) = 6$, so $a = 2$. 5. Equation: $y = 2(3)^x$. Strategic Tip: Dividing equations eliminates $a$ and isolates a power of $b$. Choice B is incorrect because $a = 2$, not 6. Choice C is incorrect because $b = 3$, not 2. Choice D is incorrect because neither value is correct.