1. The problem is to solve the equation $y = a^x$ for a given base $a > 0$ and $a \neq 1$, and then graph it. 2. The general form of the exponential function is: $$y = a^x$$ where $a$ is the base and $x$ is the exponent. 3. Important rules: - If $a > 1$, the function is increasing. - If $0 < a < 1$, the function is decreasing. - The graph passes through the point $(0,1)$ because $a^0 = 1$. 4. To plot the graph, we evaluate $y$ at several values of $x$. 5. For example, if $a=2$, then: - $y = 2^{-2} = \frac{1}{4}$ - $y = 2^{-1} = \frac{1}{2}$ - $y = 2^{0} = 1$ - $y = 2^{1} = 2$ - $y = 2^{2} = 4$ 6. The graph is an exponential curve increasing from left to right, crossing the y-axis at 1. Final answer: The function $y = 2^x$ is an exponential growth function with the described properties and graph.