1. Problem statement: Given the exponential function $f(x) = a^x$ and a point $A = (1, 2)$ on its graph, find the base $a$ of the exponential function. 2. Formula used: Since the point $(1, 2)$ lies on the curve, it satisfies the function, so: $$f(1) = a^1 = a = 2$$ 3. Explanation: The base $a$ of the exponential function is the value of the function at $x=1$. Since $f(1) = 2$, the base $a$ must be 2. 4. Conclusion: The base $a$ of the exponential function is 2. Final answer: $a = 2$