Question 21 of 49intermediate🔧 ApplyNumerical3 marks

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.

Correct Answer

After 1 hour: 111, After 2 hours: 102, After 3 hours: 93; Linear expression: 120 - 9n

Exercise: Exercise Set 2.3 | Q: 2 | (Page 9)
For More Understanding

Explanation

This problem models linear decay, where a quantity decreases by a constant value over time. The initial number of members is 120, and the constant rate of decrease is 9 members per hour. By subtracting the total number of dropouts (9 multiplied by the number of hours) from the initial count, we can find the remaining members for any given hour and derive the linear expression.

Solution Steps

  1. Step 1: Identify the initial number of members = 120.

  2. Step 2: Identify the number of members dropping out each hour = 9.

  3. Step 3: Calculate members remaining after 1 hour: 120 - (9×19 \times 1) = 111.

  4. Step 4: Calculate members remaining after 2 hours: 120 - (9×29 \times 2) = 102.

  5. Step 5: Calculate members remaining after 3 hours: 120 - (9×39 \times 3) = 93.

  6. Step 6: Form the linear expression for the nth hour by subtracting the total dropouts (9n) from the initial members (120), which gives 120 - 9n.

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