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

The function representing the situation is P(t) = $20,000 * (1 - 0.134)^t. It decreases by 13.4% each year.

Step-by-step explanation:

The function representing the situation can be expressed as:

P(t) = $20,000 * (1 - 0.134)^t

Where P(t) represents the profit after t years.

For example, if we want to calculate the profit after 5 years, we substitute t with 5 in the function:

P(5) = $20,000 * (1 - 0.134)^5

P(5) = $20,000 * (0.866)^5

P(5) ≈ $10,355.92

Answer 2

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-(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`.