# The function​ A(s) given by ​A(s)equals0.328splus50 can be used to estimate the average age of employees of a company in the years 1981 to 2009. Let​ A(s) be the average age of an​ employee, and s be the number of years since​ 1981; that​ is, sequals0 for 1981 and sequals9 for 1990. What was the average age of the employees in 2003 and in​ 2009?

The average age of the employees in 2003 is 57.216 years. And, the average age of the employees in 2009 is 59.184 years.

Given that;

The function​ A(s) given by ,

A (s) = 0.328s + 50

Now for the average age of employees in 2003 and 2009 using the function A(s) = 0.328s + 50, substitute the values of s into the equation.

For the year 2003,

Since s represents the number of years since 1981,

Hence, subtract 1981 from 2003:

s = 2003 - 1981

s = 22

Now substitute this value of s into the function A(s):

A(22) = 0.328 × 22 + 50

A(22) = 7.216 + 50

A(22) = 57.216

Therefore, the average age of the employees in 2003 is 57.216 years.

Similarly, for the year 2009,

s = 2009 - 1981

s = 28

Substituting this value into the function:

A(28) = 0.328 × 28 + 50

A(28) = 9.184 + 50

A(28) = 59.184

Hence, the average age of the employees in 2009 is 59.184 years.

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The mathematical problem involves calculating the average age of employees at a company for the years 2003 and 2009 using the linear function A(s), where 'A(s)' represents the average age and 's' is the number of years since 1981. The calculated average ages for the employees in the years 2003 and 2009 are approximately 57 and 59 years, respectively.

### Explanation:

The subject is mathematics, specifically linear functions. Based on the equation A(s) = 0.328s + 50, where 'A(s)' represents the average age of the employees and 's' represents the number of years since 1981. In the year 2003, s would be 22 (2003-1981) and in 2009, s would be 28 (2009-1981).

Substituting these values of 's' into the function gives:

For 2003, A(22) = 0.328*22 + 50 = 57.216

For 2009, A(28) = 0.328*28 + 50 = 59.184

Therefore, the average age of the employees at the company in 2003 and 2009 were approximately 57 and 59 years, respectively.

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