To analyze the projected growth of both high schools over time, we can define the functions \( A(t) \) and \( B(t) \) based on the information given.
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High School A:
- Current number of students: 900
- Growth rate: 50 students per year
The function can be defined as: \[ A(t) = 900 + 50t \]
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High School B:
- Current number of students: 700
- Growth rate: 100 students per year
The function can be defined as: \[ B(t) = 700 + 100t \]
Next, we will calculate the number of students in each high school after \( t = 2 \) years.
Calculate \( A(2) \) and \( B(2) \):
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For High School A: \[ A(2) = 900 + 50(2) = 900 + 100 = 1000 \]
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For High School B: \[ B(2) = 700 + 100(2) = 700 + 200 = 900 \]
Conclusion:
After 2 years:
- High School A is projected to have 1000 students.
- High School B is projected to have 900 students.
Therefore, High School A is projected to have more students than High School B after 2 years.
Graphing the Functions:
To visualize this, you could graph both functions \( A(t) \) and \( B(t) \) on a coordinate plane with \( t \) (years) on the x-axis and the number of students on the y-axis.
- Function \( A(t) \) would be a straight line starting from \( (0, 900) \) with a slope of 50.
- Function \( B(t) \) would also be a straight line starting from \( (0, 700) \) with a slope of 100.
The graph would show that \( B(t) \) rises faster than \( A(t) \) but started at a lower point. Over time, intersections or comparisons can be drawn at various points, including \( t = 2 \).
Overall, the growth trends suggest that although High School B has a higher growth rate per year, High School A’s larger starting population allows it to have more students after 2 years.
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