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If a disease spreads at a rate of 10% per week, what will be the total percentag

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Question: If a disease spreads at a rate of 10% per week, what will be the total percentage of the population infected after 3 weeks, assuming no recovery? (2021)

Options:

  1. 30%
  2. 33%
  3. 27%
  4. 25%

Correct Answer: 33%

Exam Year: 2021

Solution: 

Total infected after 3 weeks = 10% + 10% of (100% - 10%) + 10% of (100% - 20%) = 10% + 9% + 8% = 27%.

If a disease spreads at a rate of 10% per week, what will be the total percentag

Practice Questions

Q1
If a disease spreads at a rate of 10% per week, what will be the total percentage of the population infected after 3 weeks, assuming no recovery? (2021)
  1. 30%
  2. 33%
  3. 27%
  4. 25%

Questions & Step-by-Step Solutions

If a disease spreads at a rate of 10% per week, what will be the total percentage of the population infected after 3 weeks, assuming no recovery? (2021)
  • Step 1: Start with the initial infection rate, which is 10% of the population infected in the first week.
  • Step 2: Calculate the number of new infections in the second week. This is 10% of the remaining uninfected population. The remaining uninfected population after the first week is 100% - 10% = 90%. So, 10% of 90% is 9%.
  • Step 3: Add the new infections from the second week to the total infected so far. Total infected after 2 weeks = 10% + 9% = 19%.
  • Step 4: Calculate the number of new infections in the third week. The remaining uninfected population after the second week is 100% - 19% = 81%. So, 10% of 81% is 8.1%.
  • Step 5: Add the new infections from the third week to the total infected so far. Total infected after 3 weeks = 19% + 8.1% = 27.1%.
  • Step 6: Round the total infected percentage to the nearest whole number if necessary. In this case, it remains 27%.
  • Exponential Growth – The question tests understanding of exponential growth in the context of disease spread, where the infection rate applies to the remaining uninfected population.
  • Percentage Calculations – It requires the ability to calculate percentages of percentages over multiple time periods.
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