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Answer :
To determine the rate of decay for the given exponential function [tex]\( y = 63.4(0.92)^x \)[/tex], we need to look at the base of the exponent, which is 0.92.
In an exponential function of the form [tex]\( y = a(b)^x \)[/tex], the value [tex]\( b \)[/tex] represents the growth or decay factor:
- If [tex]\( b > 1 \)[/tex], the function represents exponential growth.
- If [tex]\( 0 < b < 1 \)[/tex], the function represents exponential decay.
Here, the base [tex]\( b = 0.92 \)[/tex], which is less than 1. This indicates that the function is experiencing exponential decay.
The decay rate [tex]\( r \)[/tex] can be found by subtracting the decay factor from 1:
[tex]\[ r = 1 - b \][/tex]
For our function:
[tex]\[ r = 1 - 0.92 = 0.08 \][/tex]
Thus, the rate of decay [tex]\( r \)[/tex] is [tex]\( 0.08 \)[/tex].
Therefore, the correct answer is:
[tex]\( r = 0.08 \)[/tex]
In an exponential function of the form [tex]\( y = a(b)^x \)[/tex], the value [tex]\( b \)[/tex] represents the growth or decay factor:
- If [tex]\( b > 1 \)[/tex], the function represents exponential growth.
- If [tex]\( 0 < b < 1 \)[/tex], the function represents exponential decay.
Here, the base [tex]\( b = 0.92 \)[/tex], which is less than 1. This indicates that the function is experiencing exponential decay.
The decay rate [tex]\( r \)[/tex] can be found by subtracting the decay factor from 1:
[tex]\[ r = 1 - b \][/tex]
For our function:
[tex]\[ r = 1 - 0.92 = 0.08 \][/tex]
Thus, the rate of decay [tex]\( r \)[/tex] is [tex]\( 0.08 \)[/tex].
Therefore, the correct answer is:
[tex]\( r = 0.08 \)[/tex]
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