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

Answer: $f(x) = 80 ( 1.1 ) ^x$

Step-by-step explanation:

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

$f(x) = ab^x$ ----- (1)

Where a and b are any unknown numbers.

For x = 0,

$f(0) = ab^0= a$

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),

$f(x) = 80000 b^x$  ------- (2)

Now again according to the question,

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

But the average annual salary in 2006 is $f(1) = 80000 b^1$

⇒ $80000 b^1=88000$

⇒ b = 1.1

Putting the value of b in equation (2),

The average annual salary after x years since 2005 is,

$f(x) = 80000 (1.1)^x$ dollars

Or  $f(x) = 80 (1.1)^x$ thousand dollars

Thus, Fourth Option is correct.

Answer 2

The answer is f(x)=80(1.1)x