1. **Problem:** Identify the type of function and write the explicit equation for the function given the table: $$\begin{array}{c|c} x & y \\ \hline 0 & 3 \\ 1 & 6 \\ 2 & 12 \\ 3 & 24 \\ 4 & 48 \\ 5 & 96 \end{array}$$ 2. **Type of function:** Exponential, because the $y$ values multiply by a constant factor as $x$ increases. 3. **Formula for exponential functions:** $$y = a \cdot b^x$$ where $a$ is the initial value (when $x=0$) and $b$ is the base or growth factor. 4. **Find $a$:** From the table, when $x=0$, $y=3$, so $a=3$. 5. **Find $b$:** Calculate the ratio between consecutive $y$ values: $$\frac{6}{3} = 2, \quad \frac{12}{6} = 2, \quad \frac{24}{12} = 2$$ So, $b=2$. 6. **Write the explicit equation:** $$y = 3 \cdot 2^x$$ **Final answer:** $$\boxed{y = 3 \cdot 2^x}$$