Answer:
Number of mice that will be infected next week
N₁ = 220
in 3 weeks
N₃ = 149.8
Step-by-step explanation:
Let A represent the number of infected mice and B represent the number of noninfected mice at a particular time.
Initially;
A₀ = 400
B₀ = 1000-400 = 600
Probability that an infected mouse will overcome the virus Pa = 60%
probability that a noninfected mouse will become infected Pb= 10%
The number of mice that would be infected in the next week is N ;
N₁ = A - APa + BPb
N₁ = 400 - 0.60(400) + 0.10(600)
N₁ = 400 - 240 + 60
N₁ = 220
Second week;
A₁ = 220
B₁ = 1000-220 = 780
N₂ = 220 - 0.60(220) + 0.10(780)
N₂ = 220 - 132 + 78
N₂ = 166
Three weeks after;
A₂ = 166
B₂ = 1000-166 = 834
N₃ = 166 - 0.60(166) + 0.10(834)
N₃ = 149.8
A₃ = 149.8
