Question

A small town has two local high schools. High School A currently has 900 studentsand is projected to grow by 50 students each year. High School B currently has 500students and is projected to grow by 100 students each year. Let A represent thenumber of students in High School A in t years, and let B represent the number ofstudents in High School B after t years. Graph each function and determine whichhigh school is projected to have more students in 4 years.

Answer 1

High School A currently has 900 students and is projected to grow by 50 students each year.

We can write an equation using the above information

`A=900+50t`

Where A represents the number of students in High School A in t years.

High School B currently has 500 students and is projected to grow by 100 students each year.

We can write an equation using the above information

`B=500+100t`

Where B represents the number of students in High School B in t years.

Let us graph these two equations

Determine which high school is projected to have more students in 4 years.

Let us substitute t = 4 into both equations

`\begin{gathered} A=900+50t \\ A=900+50(4) \\ A=900+200 \\ A=1100 \end{gathered}`

High school A is projected to have 1100 students in 4 years.

`\begin{gathered} B=500+100t \\ B=500+100(4) \\ B=500+400 \\ B=900 \end{gathered}`

High school B is projected to have 900 students in 4 years.

Therefore, high school A is projected to have more students (1100) as compared to high school B (900) in 4 years.