Question

given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.

\\( y = 56(0.91)^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 \( b \) is the base. If \( b>1 \), it's growth; if \( 0 < b < 1 \), it's decay.
Here, \( b = 0.91 \), and since \( 0 < 0.91 < 1 \), this is a decay function.

Step2: Calculate percentage rate

The formula for the rate of decay is \( r=1 - b \) (expressed as a decimal), and to get the percentage, we multiply by 100.
So, \( r = 1 - 0.91 = 0.09 \). Converting to a percentage, \( 0.09\times100 = 9\% \).

Answer:

The function represents decay with a percentage rate of decrease of \( 9\% \).