Question

The profit for a company this year was $100,000. Each year the profit increases at a rate of 1.2% per

year. Which function shows the company's profit as a function of time in years?
a. f(t) = 100,000 0.012^t
b. f(t) = 100,000(1 + 1.2)^t
c. f(t) = 100,000(1 + 0.012)^t
d. f(t) = 100,000 - 1.2^t

Answer 1

Given:

Initial profit = $100,000

Increasing rate of profit = 1.2%

To find:

The function that shows the company's profit as a function of time in years.

Solution:

The exponential growth model is defined as:

`f(t)=a(1+r)^t`

Where, a is the initial value, b is the growth rate and t is the time period.

Putting a=100,000 and r=0.012, we get

`f(t)=100,000(1+0.012)^t`

Where, t is the number of years.

Therefore, the correct option is c.