The average annual salary of the employees of a company in the year 2005 was $80,000. it increased by the same factor each year and in 2006, the average annual salary was $88,000. 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) = 88(0.88)x
f(x) = 88(1.1)x
f(x) = 80(0.88)x
f(x) = 80(1.1)x

Step-by-step explanation:

Let the function that shows the average annual salary after x years since 2005 is,

----- (1)

Where a and b are any unknown numbers.

For x = 0,

But According to the question,

The average annual salary of the employees of a company in the year 2005 was $80,000.

Therefore, f(0)=80000 dollars.

⇒ a = 80000

From equation (1),

 ------- (2)

Now again according to the question,

In 2006, the average annual salary was $88,000

But the average annual salary in 2006 is

⇒

⇒ b = 1.1

Putting the value of b in equation (2),

The average annual salary after x years since 2005 is,

dollars

Or   thousand dollars

Thus, Fourth Option is correct.

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.