A medical researcher is studying the spread of a virus in a population of 1000 laboratory mice. During any week, there is an 80% probability that an infected mouse will overcome the virus, and during the same week there is a 10% probability that a noninfected mouse will become infected. Three hundred mice are currently infected with the virus. How many will be infected next week and in 3 weeks

The number of mice that will be infected next week are 130 while

The number of mice that will be infected in 3 weeks are 111

Step-by-step explanation:

From the information given, the researcher is studying the spread of a virus in a population of 1000 laboratory mice. i. e, n = 1000

Number of infected = 300

Non infected = 1000 - 300 = 700

Probability an infected mouse will overcome = 80% = 0.8

Probability a noninfected mouse becomes infected = 10% = 0.10

The number of infected that will overcome = 0.8 * 300 = 240

The number of non infected that will become infected = 0.1 * 700 = 70

The number that will be infected on the first week =

300 - 240 + 70

= 130

Number that will be healthy on the first week =

700 + 240 - 70

= 870

Calculating for week 2:

The number of infected that will overcome = 0.8 * 130 = 104

The number of non infected that will become infected = 0.10 * 870 = 87

The number that will be infected on the second week =

130 - 104 + 87

= 113

Number that will be healthy on the second week =

870 + 107 - 87

= 887

Calculating for week 3:

The number of infected that will overcome = 0.8 * 113 = 90.4

The number of non infected that will become infected = 0.10 * 887 = 88.7

The number that will be infected on the third week =

113 - 90.4 + 88.7

= 111.3 ≈ 111

Number that will be healthy on the third week =

887 + 90.4 - 88.7

= 888.7 ≈ 889

From our calculations, the number of mice that will be infected next week are 130

The number of mice that will be infected in 3 weeks are 111