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Answer :
To find the rate of decay, [tex]\( r \)[/tex], in the exponential function [tex]\( y = 63.4(0.92)^x \)[/tex], you need to understand the components of the function:
1. The exponential function is generally in the form [tex]\( y = a \cdot b^x \)[/tex], where:
- [tex]\( a \)[/tex] is the initial value.
- [tex]\( b \)[/tex] is the base of the exponential which represents the decay factor if it's less than 1.
2. In this function, the base [tex]\( b \)[/tex] is 0.92. This tells us that it is a decay process because [tex]\( b < 1 \)[/tex].
3. The rate of decay, [tex]\( r \)[/tex], can be calculated using the formula [tex]\( r = 1 - b \)[/tex].
Now let's find [tex]\( r \)[/tex]:
- The decay factor [tex]\( b = 0.92 \)[/tex].
- To find [tex]\( r \)[/tex], use the formula [tex]\( r = 1 - b \)[/tex]:
[tex]\[
r = 1 - 0.92 = 0.08
\][/tex]
Thus, the rate of decay [tex]\( r \)[/tex] is [tex]\( 0.08 \)[/tex] (expressed as a decimal). Therefore, the correct answer is [tex]\( r = 0.08 \)[/tex].
1. The exponential function is generally in the form [tex]\( y = a \cdot b^x \)[/tex], where:
- [tex]\( a \)[/tex] is the initial value.
- [tex]\( b \)[/tex] is the base of the exponential which represents the decay factor if it's less than 1.
2. In this function, the base [tex]\( b \)[/tex] is 0.92. This tells us that it is a decay process because [tex]\( b < 1 \)[/tex].
3. The rate of decay, [tex]\( r \)[/tex], can be calculated using the formula [tex]\( r = 1 - b \)[/tex].
Now let's find [tex]\( r \)[/tex]:
- The decay factor [tex]\( b = 0.92 \)[/tex].
- To find [tex]\( r \)[/tex], use the formula [tex]\( r = 1 - b \)[/tex]:
[tex]\[
r = 1 - 0.92 = 0.08
\][/tex]
Thus, the rate of decay [tex]\( r \)[/tex] is [tex]\( 0.08 \)[/tex] (expressed as a decimal). Therefore, the correct answer is [tex]\( r = 0.08 \)[/tex].
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