1. **State the problem:** We have the function $y=2^x$ (solid line) and a dilation from the y-axis by a factor $a$ (dotted line). We need to determine if $a$ is greater than 1, less than 1, or if there is not enough information. 2. **Recall the dilation from the y-axis:** A dilation from the y-axis by a factor $a$ transforms the function $y=f(x)$ into $y=f(\frac{x}{a})$. 3. **Apply this to $y=2^x$:** The dilated function is $$y=2^{\frac{x}{a}}.$$ 4. **Analyze the effect of $a$ on the graph:** - If $a>1$, then $\frac{x}{a}$ grows slower than $x$, so $2^{\frac{x}{a}}$ grows slower than $2^x$. The dotted line will rise more gradually than the solid line. - If $a<1$, then $\frac{x}{a}$ grows faster than $x$, so $2^{\frac{x}{a}}$ grows faster than $2^x$. The dotted line will rise more steeply than the solid line. 5. **Compare with the graph description:** The dotted line rises more gradually than the solid line for positive $x$ values. 6. **Conclusion:** Since the dotted line grows more slowly, the dilation factor $a$ must be greater than 1. **Final answer:** $a > 1$ (Option A).