Question

question given the following exponential function, identify whether the change represent or decay, and determine the percentage rate of increase or decrease. \\( y = 3300(0.949)^x \\) answer attempt 1 out of 2 growth \\( \\% \\) increase submit answer

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, \( b = 0.949 \), and since \( 0 < 0.949 < 1 \), this is decay.

Step2: Calculate percentage rate of decrease

The formula for the rate of decrease \( r \) is \( b = 1 - r \), so \( r = 1 - b \).
Substitute \( b = 0.949 \): \( r = 1 - 0.949 = 0.051 \).
To convert to a percentage, multiply by 100: \( 0.051 \times 100 = 5.1\% \).

Answer:

This is decay with a \( 5.1\% \) decrease.