Answer :
To find the rate of decay, we need to look at the exponential function provided, which is [tex]\( y = 63.4(0.92)^x \)[/tex].
In an exponential function of the form [tex]\( y = A(b)^x \)[/tex], where [tex]\( A \)[/tex] is the initial amount and [tex]\( b \)[/tex] is the base:
1. If [tex]\( b > 1 \)[/tex], the function represents exponential growth.
2. If [tex]\( 0 < b < 1 \)[/tex], the function represents exponential decay.
The base [tex]\( b \)[/tex] in the given function is 0.92. Since 0.92 is less than 1, we are dealing with decay.
The rate of decay [tex]\( r \)[/tex] is calculated using the formula:
[tex]\[ r = 1 - b \][/tex]
So, plug in the value of [tex]\( b \)[/tex]:
[tex]\[ r = 1 - 0.92 = 0.08 \][/tex]
Therefore, the rate of decay [tex]\( r \)[/tex] is 0.08.
In an exponential function of the form [tex]\( y = A(b)^x \)[/tex], where [tex]\( A \)[/tex] is the initial amount and [tex]\( b \)[/tex] is the base:
1. If [tex]\( b > 1 \)[/tex], the function represents exponential growth.
2. If [tex]\( 0 < b < 1 \)[/tex], the function represents exponential decay.
The base [tex]\( b \)[/tex] in the given function is 0.92. Since 0.92 is less than 1, we are dealing with decay.
The rate of decay [tex]\( r \)[/tex] is calculated using the formula:
[tex]\[ r = 1 - b \][/tex]
So, plug in the value of [tex]\( b \)[/tex]:
[tex]\[ r = 1 - 0.92 = 0.08 \][/tex]
Therefore, the rate of decay [tex]\( r \)[/tex] is 0.08.
