1. The problem asks: What are the values of $a$ and $b$ in an exponential function of the form $$y = a \cdot b^x$$? 2. The general form of an exponential function is $$y = a \cdot b^x$$ where: - $a$ is the initial value or the value of $y$ when $x=0$. - $b$ is the base or growth/decay factor, which shows how much $y$ changes when $x$ increases by 1. 3. To find $a$, look at the value of $y$ when $x=0$ because: $$y = a \cdot b^0 = a \cdot 1 = a$$ 4. To find $b$, use two points $(x_1, y_1)$ and $(x_2, y_2)$ and solve: $$y_1 = a \cdot b^{x_1}$$ $$y_2 = a \cdot b^{x_2}$$ Divide the second equation by the first: $$\frac{y_2}{y_1} = \frac{a \cdot b^{x_2}}{a \cdot b^{x_1}} = b^{x_2 - x_1}$$ Then solve for $b$: $$b = \sqrt[x_2 - x_1]{\frac{y_2}{y_1}}$$ 5. In summary: - $a$ is the initial value (value at $x=0$). - $b$ is the growth or decay factor found by comparing $y$ values at different $x$ values. This explains what $a$ and $b$ represent in exponential functions.