Set 6: Exponential Functions (Intermediate)

Choice A is correct. Choice A is the correct answer. Use the pattern to find $a$ and $b$. 1. Initial Value: When $x=0$, $y=20$, so $a = 20$. 2. Growth Factor: From $x=0$ to $x=1$: $\frac{60}{20} = 3$. From $x=1$ to $x=2$: $\frac{180}{60} = 3$. 3. Constant Ratio: The factor $b = 3$ is consistent. 4. Equation: $y = 20(3)^x$. Strategic Tip: In exponential functions, dividing consecutive $y$-values gives you the base $b$. Choice B is incorrect because it swaps the initial value and base. Choice C is incorrect because this is a linear function, but the data shows multiplicative growth. Choice D is incorrect because the initial value doesn't match ($y \neq 60$ when $x=0$).