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 = 47(1.09)^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, \( b \) is the base. If \( b > 1 \), it's growth; if \( 0 < b < 1 \), it's decay. The percentage rate is \( (b - 1) \times 100\% \).

Step2: Analyze the given function

Given \( y = 47(1.09)^x \), here \( b = 1.09 \). Since \( 1.09 > 1 \), it's growth.

Step3: Calculate percentage rate

Percentage rate \( = (1.09 - 1) \times 100\% = 0.09 \times 100\% = 9\% \).

Answer:

The function represents growth with a percentage rate of increase of \( 9\% \).