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)
Practice Questions
1 question
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)
12.36%
10.5%
11.5%
15%
Using the formula for compound growth: Total infected = 100 × (1 - (1 - 0.03)^4) = 100 × (1 - 0.88) = 12.36%.
Questions & Step-by-step Solutions
1 item
Q
Q: 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)
Solution: Using the formula for compound growth: Total infected = 100 × (1 - (1 - 0.03)^4) = 100 × (1 - 0.88) = 12.36%.
Steps: 10
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).
