Question

given the exponential function $b(t) = 5(0.22)^t$, is the function classified as exponential growth or decay?

• the function is classified as exponential decay because the base is 0.22.
• the function is classified as exponential decay because the base is 0.78.
• the function is classified as exponential growth because the base is 1.22
• the function is classified as exponential growth because the base is 1.78

Explanation:

Step1: Recall exponential function form

The general form of an exponential function is \( y = a(b)^t \), where \( a \) is the initial value and \( b \) is the base. If \( 0 < b < 1 \), the function is exponential decay; if \( b > 1 \), it is exponential growth.

Step2: Analyze the given function

The given function is \( b(t) = 5(0.22)^t \). Here, the base \( b = 0.22 \). Since \( 0 < 0.22 < 1 \), the function represents exponential decay.

Answer:

The function is classified as exponential decay because the base is 0.22.