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

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kdmac56 kdmac56 · Answer 1 · 2017-07-24T21:05:14+02:00

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

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parmesanchilliwack parmesanchilliwack · Answer 2 · 2019-01-02T09:06:48+01:00

Answer: [tex]f(x) = 80 ( 1.1 ) ^x[/tex]

Step-by-step explanation:

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

[tex]f(x) = ab^x[/tex] ----- (1)

Where a and b are any unknown numbers.

For x = 0,

[tex]f(0) = ab^0= a[/tex]

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),

[tex]f(x) = 80000 b^x[/tex] ------- (2)

Now again according to the question,

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

But the average annual salary in 2006 is [tex]f(1) = 80000 b^1[/tex]

⇒ [tex] 80000 b^1=88000[/tex]

⇒ b = 1.1

Putting the value of b in equation (2),

The average annual salary after x years since 2005 is,

[tex]f(x) = 80000 (1.1)^x[/tex] dollars

Or [tex]f(x) = 80 (1.1)^x[/tex] thousand dollars

Thus, Fourth Option is correct.