Question

1. find the related percent increase or decrease for the functions below. f(x)=12(0.39)^x

Explanation:

Step1: Recall Exponential Formula

The general form of an exponential function is \( f(x) = a(b)^x \), where \( a \) is the initial amount, and \( b \) is the growth/decay factor. If \( b > 1 \), it's growth; if \( 0 < b < 1 \), it's decay. The percent change is calculated as \( (b - 1)\times100\% \).

Step2: Identify \( b \) and Calculate Percent Change

For \( f(x) = 12(0.39)^x \), \( b = 0.39 \). Calculate the percent change: \( (0.39 - 1)\times100\% = (-0.61)\times100\% = -61\% \). The negative sign indicates a decrease.

Answer:

The function represents a 61% decrease.