Answer :
To find the rate of decay, [tex]\( r \)[/tex], in the exponential function [tex]\( y = 63.4(0.92)^x \)[/tex], we should focus on the base of the exponential term, which is [tex]\( 0.92 \)[/tex].
In exponential decay models, the base of the exponent represents [tex]\( 1 - r \)[/tex], where [tex]\( r \)[/tex] is the rate of decay expressed as a decimal. Therefore, we can find [tex]\( r \)[/tex] by calculating:
[tex]\[ r = 1 - \text{base} \][/tex]
For this particular exponential function, the base is [tex]\( 0.92 \)[/tex]. So, the rate of decay [tex]\( r \)[/tex] is calculated as follows:
[tex]\[ r = 1 - 0.92 \][/tex]
[tex]\[ r = 0.08 \][/tex]
Therefore, the rate of decay, [tex]\( r \)[/tex], expressed as a decimal is [tex]\( \boxed{0.08} \)[/tex]. This matches one of the given options.
In exponential decay models, the base of the exponent represents [tex]\( 1 - r \)[/tex], where [tex]\( r \)[/tex] is the rate of decay expressed as a decimal. Therefore, we can find [tex]\( r \)[/tex] by calculating:
[tex]\[ r = 1 - \text{base} \][/tex]
For this particular exponential function, the base is [tex]\( 0.92 \)[/tex]. So, the rate of decay [tex]\( r \)[/tex] is calculated as follows:
[tex]\[ r = 1 - 0.92 \][/tex]
[tex]\[ r = 0.08 \][/tex]
Therefore, the rate of decay, [tex]\( r \)[/tex], expressed as a decimal is [tex]\( \boxed{0.08} \)[/tex]. This matches one of the given options.
