Answer :
To find the rate of decay, [tex]\( r \)[/tex], in the exponential function [tex]\( y = 63.4(0.92)^x \)[/tex], you can use the structure of the exponential function [tex]\( y = a(b)^x \)[/tex], where [tex]\( b \)[/tex] is the base representing the growth or decay factor.
In this particular function:
- [tex]\( a = 63.4 \)[/tex] is the initial amount.
- [tex]\( b = 0.92 \)[/tex] is the base.
For exponential decay models, the rate of decay, [tex]\( r \)[/tex], can be determined by:
[tex]\[ r = 1 - b \][/tex]
Here, we substitute the given value of [tex]\( b \)[/tex]:
1. Calculate [tex]\( r \)[/tex]:
[tex]\[ r = 1 - 0.92 \][/tex]
2. Subtract to find [tex]\( r \)[/tex]:
[tex]\[ r = 0.08 \][/tex]
So, the rate of decay [tex]\( r \)[/tex] is [tex]\( 0.08 \)[/tex].
This means that the data decreases by approximately 8% each time period. Hence, the correct answer is:
[tex]\( r = 0.08 \)[/tex].
In this particular function:
- [tex]\( a = 63.4 \)[/tex] is the initial amount.
- [tex]\( b = 0.92 \)[/tex] is the base.
For exponential decay models, the rate of decay, [tex]\( r \)[/tex], can be determined by:
[tex]\[ r = 1 - b \][/tex]
Here, we substitute the given value of [tex]\( b \)[/tex]:
1. Calculate [tex]\( r \)[/tex]:
[tex]\[ r = 1 - 0.92 \][/tex]
2. Subtract to find [tex]\( r \)[/tex]:
[tex]\[ r = 0.08 \][/tex]
So, the rate of decay [tex]\( r \)[/tex] is [tex]\( 0.08 \)[/tex].
This means that the data decreases by approximately 8% each time period. Hence, the correct answer is:
[tex]\( r = 0.08 \)[/tex].
