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) ?

Question

Mathematics

Ryan Irwin

19 June, 12:25

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) ?

+4

Answers (2)

Know the Answer?

Pamela Ballard · 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

Max Berger · 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)