Question

without graphing, determine whether the function represents exponential growth or exponential decay. then find the y-intercept.$f(x)=5(0.67)^x$choose the correct answer below.the function represents exponential decay.the function represents exponential growth.the y-intercept is . (type an integer or a decimal.)

Explanation:

Step1: Identify growth/decay factor

An exponential function has the form $f(x)=a(b)^x$, where $b$ is the base. If $0

Step2: Calculate y-intercept

The y-intercept occurs at $x=0$. Substitute $x=0$ into the function:
$f(0)=5(0.67)^0 = 5\times1 = 5$

Answer:

The function represents exponential decay.
The y-intercept is 5