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 the 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

Answer: The correct answer to this question is f(x) = 70(1.17)^x

Answer 2

`f(x)=70(1.17)^x`

Explanation:

x is time in years

f(x) represent the average annual salary in thousand dollars

We are given

The average annual salary of the employees of a company in the Year 2005 was $70,000

We can use exponential formula

`f(x)=a(b)^x`

Since, time starts from 2005

So, at x=0 , f(x)=70

we can use it

`70=a(b)^0`

`a=70`

in 2006 the average annual salary was $82,000

So, in x=2006-2005=1

f(x)=82

we can plug it and find b

`82=70(b)^1`

`b=(41)/(35)`

`b=1.17`

now, we can plug it back

and we get

`f(x)=70(1.17)^x`