Question

now find: determine whether the function represents exponential growth or decay: f(x) = 4(0.5)^x

Explanation:

Step1: Recall exponential function form

The general form of an exponential function is \( f(x) = a(b)^x \), where \( a>0 \), \( b>0 \), and \( b
eq1 \). If \( b > 1 \), it's exponential growth; if \( 0 < b < 1 \), it's exponential decay.

Step2: Identify \( b \) in the given function

For the function \( f(x)=4(0.5)^x \), we have \( a = 4 \) and \( b = 0.5 \).

Step3: Compare \( b \) with 1

Since \( 0 < 0.5 < 1 \), according to the rule of exponential functions, this function represents exponential decay.

Answer:

The function \( f(x) = 4(0.5)^x \) represents exponential decay.