Question

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

Answer 1

The equation to model the growth is of the form:
\[\large f(x)=80000(1+r)^{x}\]
where r is the growth factor.

We are given that when x = 1, f(x) = 88000
therefore we can write the following equation:
\[\large 88000=80000(1+r)\ .........(1)\]
Now you need to solve equation (1) to find the value of r.

Answer 2

88000=80000+80000r
=8000

Answer 3

88000 = 80000 + 80000r
subtract 80000 from both sides to get:
8000 = 80000r .........(2)
Now divide both sides of (2) by 80000 to get the value of r.

Answer 4

r = 8000/80000 = ?

Answer 5

10

Answer 6

No. Your result is for 80000/8000.
You need to calculate 8000/80000 = ?

Answer 7

0.1

Answer 8

Correct. r = 0.1.
So if we go back to the very first equation to model the growth and plug in the value of r, we get;
\[\large f(x)=80000(1+0.1)^{x}\]
So if we express the average salary in 2005 in thousands of dollars it becomes 80 and we get:
\[\large f(x)=80(1.1)^{x}\]

Answer 9

thanks

Answer 10

You're welcome :)