Question

Write a function in terms of t that represents the situation. A company profit of $20,000 decreases by 13.4% each year.

Answer 1

Answer:

The profit function is $P(t)=20000(0.866)^t$.

Step-by-step explanation:

The exponential decay function is defined as

$P(t)=a_0(1-r)^t$

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

$P(t)=20000(1-\frac{13.4}{100})^t$

$P(t)=20000(1-0.134)^t$

$P(t)=20000(0.866)^t$

Therefore the profit function is $P(t)=20000(0.866)^t$.