Answer:
The profit function is [tex]P(t)=20000(0.866)^t[/tex].
Step-by-step explanation:
The exponential decay function is defined as
[tex]P(t)=a_0(1-r)^t[/tex]
Where, a₀ is initial value, r is rate of change and t is time (in year).
From the given information it is noticed that the initial profit is $20,000 and it decreases by 13.4% each year.
The profit function is defined as
[tex]P(t)=20000(1-\frac{13.4}{100})^t[/tex]
[tex]P(t)=20000(1-0.134)^t[/tex]
[tex]P(t)=20000(0.866)^t[/tex]
Therefore the profit function is [tex]P(t)=20000(0.866)^t[/tex].
