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The finance manager at a college noticed that the average salary of the faculty members has been increasing for the past 10 years.

The average salary, in thousands of dollars, for arts and humanities faculty is modeled by function f, where x is the number of years since the manager began recording the data.

Answer 1

As x approaches positive infinity, the average salary for science and engineering faculty will eventually be greater than the average salary for arts and humanities faculty.

Explanation:

First consider the f(x) values on the graph as x increases on the interval 0 to 10 years. The average salary increases over the entire interval and reaches a maximum value of approximately $66,000.

Next create a table to show the values for function g.

0 16,188

1 18,366

2 21,101

3 25,000

4 40,000

5 55,000

6 58,899

7 61,634

8 63,811

9 65,650

10 67,257

The maximum value of function g is greater than the maximum value of function f. Therefore, as x approaches positive infinity, the average salary for science and engineering faculty will eventually be greater than the average salary for arts and humanities faculty.