1. The problem asks to complete a chart analyzing characteristics of three exponential functions: $y=(2.5)^x$, $y=4(2)^x$, and $y=3\left(\frac{1}{2}\right)^x$. 2. The general form of an exponential function is $y = ab^x$, where: - $a$ is the initial value or vertical stretch/compression factor. - $b$ is the base, which determines growth ($b>1$) or decay ($00$, range is $(0, \infty)$; if $a<0$, range is $(-\infty, 0)$. - The y-intercept occurs at $x=0$, so $y=a b^0 = a$. 3. Analyze each function: **For** $y = (2.5)^x$: - $a=1$ (since no coefficient in front) - $b=2.5$ - Domain: $(-\infty, \infty)$ - Range: $(0, \infty)$ since $a=1>0$ - Coordinates of intercept: $(0, 1)$ **For** $y = 4(2)^x$: - $a=4$ - $b=2$ - Domain: $(-\infty, \infty)$ - Range: $(0, \infty)$ since $a=4>0$ - Coordinates of intercept: $(0, 4)$ **For** $y = 3\left(\frac{1}{2}\right)^x$: - $a=3$ - $b=\frac{1}{2}$ - Domain: $(-\infty, \infty)$ - Range: $(0, \infty)$ since $a=3>0$ - Coordinates of intercept: $(0, 3)$ 4. The graph/table shape for all is increasing for $b>1$ and decreasing for $0