Question

There were 900 students enrolled in a high school in 2009 and 1,500 students enrolled in the same high school in 2012. The student enrollment of the high school, P, has increased at a constant rate each year, t, since 2009.

A) Write the given enrollment numbers as a pair of points in the form (t, P).
B) Find the slope of the line passing through the pair of points from part A and explain the information the slope gives about the situation.
C) Write an equation that relates the high school's student enrollment, P, to the number of years since 2009, t.
D) Predict the high school's enrollment in 2017.

Answer 1

Answer: A)
`(0,900)\ and\ (3,1500)`

B) Slope=200, It means enrollment of 200 students increases each year.

C)
`P=200t+900`

D) 2500 students.

Explanation:

Given: The student enrollment of the high school, P, has increased at a constant rate each year, t, since 2009.

At 2009, t=0 and at 2012, t=3 [Since 2012-2009=3 years]

A) In points , the given enrollment numbers will be written as:-

`(0,900)\ and\ (3,1500)`

B) The slope of the line passing through
`(0,900)\ and\ (3,1500)` is given by:-

`m=(y_2-y_1)/(x_2-x_1)=(1500-900)/(3-0)=(600)/(3)=200`

It means enrollment of 200 students increases each year.

C) The linear equation with slope= 200 and and the initial number of students (900) is given by

`P=200t+900`

D) At 2017, t=8 [Since 2017-2009=8]

Then
`P=200(8)+900=1600+900=2500`

The high school's enrollment in 2017 = 2500 students.