The first - and second-year enrollment values for a technical school are shown in the table below: Enrollment at a Technical School Year (x) First Year f (x) Second Year s (x) 2009 785 756 2010 740 785 2011 690 710 2012 732 732 2013 781 755 Which of the following statements is true based on the data in the table? The solution to f (x) = s (x) is x = 2012. The solution to f (x) = s (x) is x = 732. The solution to f (x) = s (x) is x = 2011. The solution to f (x) = s (x) is x = 710.

The solution to f (x) = s (x) is x = 2012.

Explanation:

Rewrite the table and the choices for better understanding:

Enrollment at a Technical School

Year (x) First Year f (x) Second Year s (x)

2009 785 756

2010 740 785

2011 690 710

2012 732 732

2013 781 755

Which of the following statements is true based on the data in the table?

The solution to f (x) = s (x) is x = 2012. The solution to f (x) = s (x) is x = 732. The solution to f (x) = s (x) is x = 2011. The solution to f (x) = s (x) is x = 710.

Solution

The question requires to find which of the options represents the solution to f (x) = s (x).

That means that you must find the year (value of x) for which the two functions, the enrollment the first year, f (x), and the enrollment the second year s (x), are equal.

The table shows that the values of f (x) and s (x) are equal to 732 (students enrolled) in the year 2012, x = 2012.

Thus, the correct choice is the third one:

The solution to f (x) = s (x) is x = 2012.