Linear Equations:

Question

Linear Equations

A small college had 2546 stusddents enrolled in courses in 2007. In 2012 there were 2702 students enrolled.

Assume the enrollment follows a a linear growth pattern. Let N be the number of students enrolled in the college after t years since 2005.

​a) Find an equation to show the linear relationship between N and t.

​b) In what year will the enrollment first exceed over 3000​ students?

Answer 1

t represents the number of years after 2005 so in 2007, t = 2 and N = 2546

In 2012, t = 7 as it is seven years after 2005 and N = 2702.

This of this as ordered pairs but instead of x and y you have t and N,

You need a slope so instead of (y₂- y₁)/(x₂-x₁) =m, you now have m = (N₂-N₁)/(t₂-t₁)

m = (2702-2546)/(7-2) or 31.2.

Normally, you'd use the slope point equation for a line y-y₁ = m(x - x₁) but we are using N for y and t for x.

Pick one or the pairs of values, say t=2 and N =2546

N-2546=31.2 (t-2) and solve for N= 31.2 t+2483.6..

Then substitute in 3000 for N to find the time it reaches 3000. Remember to add your answer to 2005 since t is the number of years past 2005.