1. **State the problem:** We need to find the equation of the exponential function graphed, given points (0,1), (1,4), and (2,16). 2. **Recall the general form of an exponential function:** $$y = a \cdot b^x$$ where $a$ is the initial value (value at $x=0$) and $b$ is the base or growth factor. 3. **Use the point (0,1) to find $a$:** Substitute $x=0$ and $y=1$: $$1 = a \cdot b^0 = a \cdot 1 = a$$ So, $a = 1$. 4. **Use the point (1,4) to find $b$:** Substitute $x=1$ and $y=4$: $$4 = 1 \cdot b^1 = b$$ So, $b = 4$. 5. **Check with point (2,16):** Substitute $x=2$: $$y = 1 \cdot 4^2 = 16$$ This matches the given point, confirming our values. 6. **Write the final equation:** $$y = 1 \cdot 4^x = 4^x$$ **Answer:** The equation of the exponential function is $y = 4^x$.