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:

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

Step-by-step 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

$82=70(b)^1$

$b=\frac{41}{35}$

$b=1.17$

now, we can plug it back

and we get

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

Answer 2

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