Choice A is the correct answer. Use both points to find $b$.

1. Find $a$: At $(0, 50)$, $a(b)^0 = a = 50$.
2. Find $b$: At $(2, 200)$, $50(b)^2 = 200$.
3. Solve: $b^2 = 4$, so $b = 2$ (positive).

💡 Strategic Tip: Once you know $a$, substitute the second point to solve for $b$.

Choice B is incorrect because this is $b^2$, not $b$. Choice C is incorrect because this is the initial value $a$. Choice D is incorrect because this is the $y$-value at $x=2$.