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balu736 [363]
3 years ago
7

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
Mathematics
2 answers:
SIZIF [17.4K]3 years ago
5 0

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.


Kryger [21]3 years ago
4 0
The answer is f(x)=80(1.1)x
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