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)
2,488
2,000
2,400
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.
