Question

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

( y = 650(0.05)^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, \( a = 650 \) and \( b = 0.05 \). Since \( 0 < 0.05 < 1 \), this is a decay function.

Step2: Calculate percentage rate of decrease

The formula for the rate of decrease is \( r = 1 - b \) (expressed as a percentage, we multiply by 100).
So, \( r = 1 - 0.05 = 0.95 \). To get the percentage, \( 0.95 \times 100 = 95\% \).

Answer:

The function represents decay with a percentage rate of decrease of \( 95\% \).