Question

In a population of 400,000 people, 160,000 are infected with a virus. After a person becomes infected and then recovers, the person is immune (cannot become infected again). Of the people who are infected, 4% will die each year and the others will recover. Of the people who have never been infected, 15% will become infected each year. How many people will be infected in 4 years

Answer 1

Number of people that will be infected in 4 years is 252,610.

Explanation:

The number of people that will be infected in 4 years can be calculated as follows:

Number of people that will be infected in year 1 = 160,000

Number of people that will not be infected in year 1 = 400,000 - 160,000 = 240,000

Number of people that will be infected in year 2 = Number of people that will not be infected in year 1 * 15% = 240,000 * 15% = 36,000

Number of people that will not be infected in year 2 = Number of people that will not be infected in year 1 - Number of people that will be infected in year 2 = 240,000 - 36,000 = 204,000

Number of people that will be infected in year 3 = Number of people that will not be infected in year 2 * 15% = 204,000 * 15% = 30,600

Number of people that will not be infected in year 3 = Number of people that will not be infected in year 2 - Number of people that will be infected in year 3 = 204,000 - 30,600 = 173,400

Number of people that will be infected in year 4 = Number of people that will not be infected in year 3 * 15% = 173,400 * 15% = 26,010

Therefore, we have:

Number of people that will be infected in 4 years = Number of people that will be infected in year 1 + Number of people that will be infected in year 2 + Number of people that will be infected in year 3 + Number of people that will be infected in year 4 = 160,000 + 36,000 + 30,600 + 26,010 = 252,610