SOLUTION: A small college has 3874 students in 2016 and 4798 students in 2017. If the enrollment follows a linear growth pattern find a linear function to represent the growth and find how m

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A small college has 3874 students in 2016 and 4798 students in 2017. If the enrollment follows a linear growth pattern find a linear function to represent the growth and find how m      Log On


   

Question 1098161: A small college has 3874 students in 2016 and 4798 students in 2017. If the enrollment follows a linear growth pattern find a linear function to represent the growth and find how many students the college should expect for 2018.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in years plotted on
horizontal axis
Let +E+ = number of students in the
college at any prticular time
-------------------------------------
1916 = +0+
1917 = 1+
1918 = +2+
You are given 2 points on the line, ( t,E )
( 0, 3874 )
( 1, 4798 )
----------------
Use the general point-slope formula:
+%28+E+-+3874+%29+%2F+%28+t+-+0+%29+=+%28+4798+-+3874+%29+%2F+%28+1+-+0+%29+
+%28+E+-+3874+%29+%2F+t+=+924+%2F+1+
+E+-+3874+=+924t+
+E+=+924t+%2B+3874+
------------------------
Check:
Does it go through ( 0, 3874 ) ?
+3874+=+924%2A0+%2B+3874+
+3874+=+3874+
OK
Does it go through ( 1, 4798 ) ?
+4798+=+924%2A1+%2B+3874+
+4798+=+4798+
OK
------------------------------
2018 = +2+
( E, 2 ) solve for +E+
+E+=+924%2A2+%2B+3874+
+E+=+1848+%2B+3874+
+E+=+5722+
They should expect 5722 students for 2018
----------------------------------------
check the math