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What is the rate of decay, [tex] r [/tex] (expressed as a decimal), for data best modeled by the exponential function [tex] y = 63.4(0.92)^{x} [/tex]?

A. [tex] r = 36.6 [/tex]
B. [tex] r = 0.92 [/tex]
C. [tex] r = 0.08 [/tex]
D. [tex] r = 63.4 [/tex]

Answer :

We start with the given exponential function

[tex]$$
y = 63.4 \cdot (0.92)^t.
$$[/tex]

For an exponential decay model written in the form

[tex]$$
y = A \cdot (1 - r)^t,
$$[/tex]

the base of the exponent is [tex]$(1 - r)$[/tex], which represents the factor by which the quantity decreases each time period. Here, it is clear that

[tex]$$
(1 - r) = 0.92.
$$[/tex]

To find the decay rate [tex]$r$[/tex], we solve the equation:

[tex]$$
r = 1 - 0.92.
$$[/tex]

Thus,

[tex]$$
r = 0.08.
$$[/tex]

So, the decay rate, expressed as a decimal, is [tex]$0.08$[/tex].

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Rewritten by : Jeany

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