The exponential decay function can be written as :
[tex]f(t)=P(1-r)^t[/tex]
where P = initial amount
r = rate of decay (decreasing value)
t = time in years
From the problem, we have :
P = $32,000
r = 16.5% or 0.165
The function will be :
[tex]\begin{gathered} f(t)=32000(1-0.165)^t \\ f(t)=32000(0.835)^t \end{gathered}[/tex]
Using desmos, the graph of the function will be :
Then use the graph to predict when the value will fall to $3000
That will be :
in about 13 years, the value will fall to $3000
ANSWER :
The function is :
[tex]f(t)=32000(0.835)^t[/tex]
The value will fall to $3000 in about 13 years.
