Answer: D

An exponential function has the form $g(x) = a(b)^x$. Since $g(0) = a = 12$, $g(x) = 12(b)^x$. Then $g(2) = 12b^2 = 3$, so $b^2 = \frac{1}{4}$ and $b = \frac{1}{2}$, because $b$ is positive. So $g(x) = 12\left(\frac{1}{2}\right)^x$.

Choice C uses $\frac{3}{12} = \frac{1}{4}$ as the base, but that is the factor over $2$ steps, which is $\frac{1}{2} \cdot \frac{1}{2}$.

Why the other choices are wrong

• A. This linear function matches both points, but the question says g is exponential.
• B. This uses g(2) = 3 as the starting value. The starting value is g(0) = 12.
• C. 1/4 is the factor over 2 steps. The factor for each step is the square root of 1/4, which is 1/2.