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)?

Answer 1

Options: 
(A) f(x) = 70(1.17)^x
(B) f(x) = 82(1.17)^x
(C) f(x) = 70(2.2)^x
(D) f(x) = 82(2.2)^x
Base is 2005 salary, 70,000.

Change is 82,000/70,000 = 1.17

Correct answer is: A) f(x) = 70(1.17)^x

Answer 2

We can make use of the general formula for the geometric series to generate the function representing the average annual salary.
an = a0(r)^(n-1)

Or
f(x) = a0(r)^(x - 1)

Plugging in the given values for the year 2005 and 2006 to ge the value of r.
82000 = 70000 (r)^(1-1)
r = 1.1714

Therefore, the function is:
f(x) = 70,000 (1.1714)^(x-1)