To determine the rate of decay in an exponential function of the form [tex]\( y = a(b)^x \)[/tex], we need to focus on the base [tex]\( b \)[/tex] of the exponential term [tex]\( (b)^x \)[/tex].
Consider the given equation:
[tex]\[ y = 63.4(0.92)^x \][/tex]
In this equation, [tex]\( 63.4 \)[/tex] is the initial value or the coefficient [tex]\( a \)[/tex], and [tex]\( 0.92 \)[/tex] is the base [tex]\( b \)[/tex] of the exponential term. The base [tex]\( b \)[/tex] represents the growth or decay factor.
1. Identify the base [tex]\( b \)[/tex]:
[tex]\[ b = 0.92 \][/tex]
2. Since [tex]\( b \)[/tex] is less than 1, the function represents an exponential decay. The rate of decay, [tex]\( r \)[/tex], can be directly identified as the base of the exponent, which is [tex]\( 0.92 \)[/tex].
Thus, the rate of decay, [tex]\( r \)[/tex], expressed as a decimal, is:
[tex]\[ r = 0.92 \][/tex]
Therefore, the correct answer is:
[tex]\[ r = 0.92 \][/tex]
