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A national festival lasts for 5 days. If the attendance increases by 20% each da

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Question: A national festival lasts for 5 days. If the attendance increases by 20% each day starting from 1,000 on the first day, what is the attendance on the fifth day? (2073)

Options:

  1. 2,488
  2. 2,000
  3. 2,400
  4. 2,500

Correct Answer: 2,488

Exam Year: 2073

Solution: 

Attendance on the fifth day = 1000 * (1 + 0.20)^4 = 1000 * 2.0736 = 2073.6 ≈ 2074.

A national festival lasts for 5 days. If the attendance increases by 20% each da

Practice Questions

Q1
A national festival lasts for 5 days. If the attendance increases by 20% each day starting from 1,000 on the first day, what is the attendance on the fifth day? (2073)
  1. 2,488
  2. 2,000
  3. 2,400
  4. 2,500

Questions & Step-by-Step Solutions

A national festival lasts for 5 days. If the attendance increases by 20% each day starting from 1,000 on the first day, what is the attendance on the fifth day? (2073)
  • Step 1: Start with the initial attendance on the first day, which is 1,000.
  • Step 2: Understand that the attendance increases by 20% each day. This means each day, the attendance is multiplied by 1.20 (which is 100% + 20%).
  • Step 3: To find the attendance on the fifth day, we need to calculate the increase for four days (since the first day is already given).
  • Step 4: Use the formula: Attendance on the fifth day = Initial attendance * (1 + increase rate)^(number of days). Here, the increase rate is 0.20 and the number of days is 4.
  • Step 5: Plug in the numbers: Attendance on the fifth day = 1000 * (1 + 0.20)^4.
  • Step 6: Calculate (1 + 0.20) = 1.20.
  • Step 7: Raise 1.20 to the power of 4: 1.20^4 = 2.0736.
  • Step 8: Multiply this result by the initial attendance: 1000 * 2.0736 = 2073.6.
  • Step 9: Since attendance must be a whole number, round 2073.6 to the nearest whole number, which is 2074.
  • Exponential Growth – The problem tests understanding of exponential growth where a quantity increases by a fixed percentage over a series of time intervals.
  • Compound Interest Formula – The formula used (A = P(1 + r)^n) is similar to that used in calculating compound interest, where P is the initial amount, r is the rate of increase, and n is the number of periods.
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