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].
[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].