Question

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

Answer 1

Red line: function A(t)

Blue line: function B(t)

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

Step-by-step explanation

We have,

• A: number of students in school A after t years

,

• B: number of students in school B after t years

School A is projected to have 50 more students each year, while school B is projected to have 100 more students each year. Thus, both functions are linear.

High school A starts with 900 students and each year it will have 50 more,

`A(t)=900+50t`

On the other hand, high school B starts with 500 students and each year will have 100 more,

`B(t)=500+100t`

In 4 years each school will have,

`A(4)=900+50\cdot4=900+200=1100`
`B(4)=500+100\cdot4=500+400=900`

The graphs of each function are lines. The graph of A is a line passing through points (0, 900) - which is the y-intercept, and (4, 1100).

The graph of B is a line passing through points (0, 500) and (4, 900).

From these calculations and from the graph, we can see that function A has a higher value than function B at t = 4. Hence High School A is projected to have more students in 4 years.