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)
30%
33%
27%
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.
