QUESTION 2
Easy
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.
SOLUTION
1
Identify initial number and hourly decrease
Initial members \( = 120\)
Each hour, \( 9 \) members drop out (so subtract \(9\) each hour).
Each hour, \( 9 \) members drop out (so subtract \(9\) each hour).
2
Find members at the end of each hour
After \(1 \) hour : \(120 - 9 = 111\)
After \(2 \) hours : \(111 - 9 = 102\)
After \(3 \) hours : \(102 - 9 = 93\)
So we have: \(111,102,93,\)...
After \(2 \) hours : \(111 - 9 = 102\)
After \(3 \) hours : \(102 - 9 = 93\)
So we have: \(111,102,93,\)...
3
Derive linear expression for \(n{th}\) hour
After \(n\) hours, the rally has lost \(9n\) members
Members remaining \(= 120 - 9n\)
Members remaining \(= 120 - 9n\)
🏆
Final Answer :
Members remaining after \(1,2,3\),... hours: \(111,102,93,\)...
Linear Expression: \( 120 − 9n\)
Concept Note
If starting value \(= a\) and constant decrease per period \(= d\), then after \(n\) periods:
\(Value = a − d × n\)