Question

(exploring exponential functions lc)
what is the percent rate of change in the function $y = 18(1 - 0.26)^x$?
126%
74%
26%
18%

Explanation:

Step1: Recall exponential decay formula

The general form of an exponential decay function is \( y = a(1 - r)^x \), where \( r \) is the rate of decay (as a decimal), and \( 1 - r \) is the decay factor.

Step2: Identify \( r \) from the given function

In the given function \( y = 18(1 - 0.26)^x \), we can see that \( 1 - r = 1 - 0.26 \). So, \( r = 0.26 \).

Step3: Convert \( r \) to a percentage

To convert the decimal \( r = 0.26 \) to a percentage, we multiply by 100: \( 0.26\times100 = 26\% \). This represents the percent rate of change (decay rate in this case).

Answer:

26% (corresponding to the option "26%")