Question

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

$y = 14(1.49)^x$

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. The percentage rate of change is \( (b - 1)\times100\% \).

Step2: Analyze the base

For the function \( y = 14(1.49)^x \), the base \( b = 1.49 \). Since \( 1.49>1 \), this is exponential growth.

Step3: Calculate the percentage rate

To find the percentage rate, use the formula \( (b - 1)\times100\% \). Substitute \( b = 1.49 \): \( (1.49 - 1)\times100\% = 0.49\times100\% = 49\% \).

Answer:

This is exponential growth with a percentage rate of increase of \( 49\% \).