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)?

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)

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shivishivangi1679 shivishivangi1679 · Answer 2 · 2022-07-04T05:58:22-04:00

The function best represents the relationship between x and f(x) will be $f(x) = 70,000 (1.1714)^{x-1}$.

What is a function?

A function is defined as a relation between the set of inputs having exactly one output each.

The general formula for the geometric series to generate the function represents the average annual salary.

$a_n = a_0(r)^{n-1}$

Or

$f(x) = a_0(r)^{x - 1}$

The values for the years 2005 and 2006 to get the value of r.

$82000 = 70000 (r)^{1-1}\\r = 1.1714$

Therefore, the function will be:

$f(x) = 70,000 (1.1714)^{x-1}$

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