To determine the rate of decay for the given exponential function [tex]\( A(t) = P \times 0.91 \)[/tex], follow these steps:
1. Identify the base of the exponent: In the given function [tex]\( A(t) = P \times 0.91 \)[/tex], the base of the exponential expression is [tex]\( 0.91 \)[/tex].
2. Calculate the decay rate: The decay rate is found by examining how the base deviates from 1. Specifically, if the base [tex]\( b \)[/tex] is less than 1, the decay rate can be found by subtracting [tex]\( b \)[/tex] from 1 and then expressing it as a percentage.
3. Perform the subtraction:
[tex]\[
\text{Decay rate} = 1 - 0.91
\][/tex]
4. Express as a percentage:
[tex]\[
\text{Decay rate} = (1 - 0.91) \times 100
\][/tex]
5. Simplify the expression:
[tex]\[
(1 - 0.91) \times 100 = 0.09 \times 100 = 9\%
\][/tex]
Therefore, the rate of decay for the function [tex]\( A(t) = P \times 0.91 \)[/tex] is [tex]\( 9\% \)[/tex].
The correct answer is:
9%
