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If a disease spreads at a rate of 3% per week, what will be the total percentage

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Question: If a disease spreads at a rate of 3% per week, what will be the total percentage of the population infected after 4 weeks, assuming no recovery? (2021)

Options:

  1. 12.36%
  2. 10.5%
  3. 11.5%
  4. 15%

Correct Answer: 12.36%

Exam Year: 2021

Solution: 

Using the formula for compound growth: Total infected = 100 × (1 - (1 - 0.03)^4) = 100 × (1 - 0.88) = 12.36%.

If a disease spreads at a rate of 3% per week, what will be the total percentage

Practice Questions

Q1
If a disease spreads at a rate of 3% per week, what will be the total percentage of the population infected after 4 weeks, assuming no recovery? (2021)
  1. 12.36%
  2. 10.5%
  3. 11.5%
  4. 15%

Questions & Step-by-Step Solutions

If a disease spreads at a rate of 3% per week, what will be the total percentage of the population infected after 4 weeks, assuming no recovery? (2021)
  • Step 1: Understand that the disease spreads at a rate of 3% per week.
  • Step 2: Recognize that this is a compound growth problem, where the infection rate compounds over time.
  • Step 3: Convert the percentage rate to a decimal for calculations: 3% = 0.03.
  • Step 4: Identify the number of weeks we are looking at, which is 4 weeks.
  • Step 5: Use the formula for compound growth: Total infected = 100 × (1 - (1 - infection rate)^number of weeks).
  • Step 6: Plug in the values: Total infected = 100 × (1 - (1 - 0.03)^4).
  • Step 7: Calculate (1 - 0.03) = 0.97.
  • Step 8: Raise 0.97 to the power of 4: 0.97^4 = 0.8858 (approximately).
  • Step 9: Calculate 1 - 0.8858 = 0.1142 (approximately).
  • Step 10: Multiply by 100 to find the total percentage infected: 100 × 0.1142 = 11.42% (approximately).
  • Compound Growth – The question tests the understanding of compound growth, where the infection rate compounds over multiple periods.
  • Exponential Growth – It also assesses the ability to apply exponential growth concepts to a real-world scenario involving disease spread.
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