Question

exponential decay functions
analyzing exponential decay graphs
analyze the graph of the exponential decay function
the initial value is
the base, or rate of change, is
the domain is

Explanation:

Step1: Identify initial value

The initial value of an exponential function $f(x) = a(b)^x$ is the value at $x=0$, which is the y-intercept. From the graph, when $x=0$, $y=2$.

Step2: Determine decay base

Use a point $(x,y)$ on the graph, e.g., $(1,1)$. Substitute $a=2$, $x=1$, $y=1$ into $f(x)=a(b)^x$:
$1 = 2(b)^1$
Solve for $b$: $b = \frac{1}{2}$

Step3: State asymptote

Exponential decay functions of the form $f(x)=a(b)^x$ (where $0

Answer:

The initial value is 2
The base, or rate of change, is $\frac{1}{2}$
The asymptote is $y=0$