A school opened in 1980 with an enrollment of 1000 students

A school opened in 1980 with an enrollment of 1000 students. In 2000, the enrollment has risen to 1500 students. Assume that the enrollment is approximately linear. Express enrollment as a function of the year. What is the slope of the graph and what does the slope represent? What is the y-intercept of the graph and what does it represent?

Solution

let year 1980= t=0

and year 2000 is t=2000-1980=20

Given no of studnts in year 1980 ie at t=0, N(0)=1000

and no of studnts in year 2000 ie at t=0, N(20)=1500

(a) Let the number of students in t year=N(t)=N(0)+at=1000+at, where \'a\' is the slope

(b)N(20)=1500=1000+a*20

=> a=500/20=25, slope representing that No of students increasing with the rate 25 every year

(c)y- intersept, means x=0

here N(t) is represent y axis and t represent x-axis

so, y intersept means x=0

that is N(t) when t=0

therfore N(0)=1000, initial no of student