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 y represent the average annual salary, in thousand dollars, after x years since 2005. Which of the following best represents the relationship between x and y?

y = 88(0.88)x
y = 88(1.1)x
y = 80(0.88)x
y = 80(1.1)x

Answer 1

Let's break down the information provided:

In the year 2005, the average annual salary was $80,000.

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

The problem states that the salary increased by the same factor each year. To represent this relationship between x (the number of years since 2005) and y (the average annual salary in thousand dollars), we can use the formula:

y = 80(1.1)^x

Here's why:

The initial salary in 2005 is $80,000, which corresponds to 80 in the formula.

The salary increased by the same factor each year, which is 1.1 (an increase of 10% or 0.1 as a decimal) because $80,000 increased to $88,000.

So, the correct relationship is:

y = 80(1.1)^x

Therefore, the correct option is:

y = 80(1.1)^x