Chapter 2: Introduction to Linear Polynomials
Chapter 2: Introduction to Linear Polynomials
Exercise
Question
Question: 2
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A rally starts with 120 members. Each hour, 9 members drop out of the group.
How many members will remain after 1, 2, 3, ... hours? Find a linear expression to represent the number of members at the end of the nth hour.
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Answer
1
Find the number of members remaining at the end of each hour.
Answer: The number of members remaining at the end of each hour is:
After 1 hour: 120 - 1 × 9 = 120 - 9 = 111
After 2 hours: 120 - 2 × 9 = 120 - 18 = 102
After 3 hours: 120 - 3 × 9 = 120 - 27 = 93
2
Use the pattern to write a linear expression for the number of members remaining at the end of the nth hour.
Answer: Number of members remaining after $n$ hours = $120 - 9n$
Reason: The group starts with 120 members, and 9 members drop out each hour. After $n$ hours, $9n$ members will have dropped out. Therefore, the number of members remaining is $120 - 9n$.