analyze the graph of the exponential decay function. the initial value is. the base, or rate of change, is…

Explanation:

Step1: Find initial - value

The initial value of an exponential function $y = ab^x$ is the value of $y$ when $x = 0$. From the points on the graph, when $x = 0$, $y=1$.

Step2: Find the base

For an exponential function $y = ab^x$, using two points $(x_1,y_1)$ and $(x_2,y_2)$. Let $(x_1,y_1)=(0,1)$ and $(x_2,y_2)=(1,\frac{1}{3})$. Substitute into $y = ab^x$, we get $y_1=ab^{x_1}$ and $y_2=ab^{x_2}$. Since $a = 1$ (from initial - value when $x = 0$), and $y_2=ab^{x_2}$, substituting $x_2 = 1$ and $y_2=\frac{1}{3}$ and $a = 1$ gives $\frac{1}{3}=1\times b^1$, so $b=\frac{1}{3}$.

Step3: Find the domain

The domain of an exponential function $y = ab^x$ is all real numbers because we can substitute any real - number value for $x$.

Answer:

The initial value is $1$. The base, or rate of change, is $\frac{1}{3}$. The domain is all real numbers.