904jasmineidn
Answered

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Given the exponential function for compounding interest, [tex]\( A(t) = P (0.82)^t \)[/tex], what is the rate of decay?

A. 18%
B. 8%
C. 0.82%
D. 82%

Sagot :

GinnyAnsweridn
To find the rate of decay in the exponential function [tex]\( A(t) = P(0.82)^t \)[/tex], we need to analyze the base of the exponent:

1. The base of the exponent, which is 0.82, represents the remaining fraction of the quantity after each time period.
2. To determine the decay rate, we identify how much the quantity decreases in each time period.
3. We start by subtracting the base of the exponent from 1. Mathematically, this is represented as:
[tex]\[ 1 - 0.82 \][/tex]

4. Calculating the above, we have:
[tex]\[ 1 - 0.82 = 0.18 \][/tex]

5. The result 0.18 represents the fraction of the quantity that decays each time period.
6. To express this as a percentage, we multiply by 100:
[tex]\[ 0.18 \times 100 = 18 \% \][/tex]

Thus, the rate of decay is [tex]\( 18 \% \)[/tex].

Therefore, the correct answer is:
[tex]\[ 18 \% \][/tex]
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