Question

question given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. $y = 28(1.01)^x$

Explanation:

Step1: Recall exponential function form

The general form of an exponential function is \( y = a(b)^x \), where \( a \) is the initial amount, and \( b \) determines growth or decay. If \( b>1 \), it's growth; if \( 0 < b < 1 \), it's decay. The percentage rate is \( (b - 1)\times100\% \).

Step2: Analyze the given function

Given \( y = 28(1.01)^x \), here \( b = 1.01 \). Since \( 1.01>1 \), it's growth.

Step3: Calculate the percentage rate

The percentage rate of increase is \( (1.01 - 1)\times100\% = 0.01\times100\% = 1\% \).

Answer:

The function represents growth with a percentage rate of increase of \( 1\% \).