Question

The average annual salary of the employees of a company in the year 2005 was $70,000. It increased by the same factor each year and in 2006, the average annual salary was $82,000. Let f(x) represent the average annual salary, in thousand dollars, after x years since 2005. Which of the following best represents the relationship between x and f(x)?

f(x) = 70(1.17)x

f(x) = 82(1.17)x

f(x) = 70(2.2)x

f(x) = 82(2.2)x

Answer 1

82/70=1.17 approx. This is the annual growth factor. After x years the growth is 1.17ˣ. The growth has to be applied to the salary in the start year 2005, when it was $70,000. So f(x)=70(1.17)ˣ, answer 1.

Answer 2

The best option that represents the relationship between the years x and the annual salary in thousand of dollar f (x) is f(x)=70*1.17^x (first option)

Explanation:

An increment function can be expressed as the initial value A times, the increment rate r raised to the amount of time x:

f(x)=A.r^x

In this particular case, the initial value is the initial salary in 2005 and the amount of time will be the years.

The annual increment rate of the salary can be found by the rate of the salary in 2006 and the salary of 2005:

r=82000/70000=1.17

Replacing the initial salary in thousands of dollars:

f(x)=70.1.17^x