1. **State the problem:** We are given a table of values for $x$ and $y$ and need to find the exponential function $y = a \cdot b^x$ that fits the data. 2. **Recall the general form:** The exponential function is $y = a \cdot b^x$, where $a$ is the initial value (when $x=0$) and $b$ is the growth factor. 3. **Identify $a$ from the table:** When $x=0$, $y=400$, so $a=400$. 4. **Find $b$ using another point:** Use $x=1$, $y=1700$. $$1700 = 400 \cdot b^1$$ Divide both sides by 400: $$\frac{1700}{400} = \cancel{\frac{400}{400}} \cdot b$$ $$4.25 = b$$ 5. **Verify with another point:** Check $x=2$, $y=7225$. Calculate $400 \cdot (4.25)^2 = 400 \cdot 18.0625 = 7225$, which matches the table. 6. **Conclusion:** The exponential function is $$y = 400 \cdot (4.25)^x$$ This matches the second option. **Final answer:** $y = 400(4.25)^x$