Propotional growth in difference equations

Question

X_n denoting the number of affected children after n weeks. Initially 2 children were affected and 3 more reported affected in the first week of the outbreak.

I know X₀ = 2 but I am confused with X₁=?

X₁ = 5 or X₁ = 3 ??

Answer 1

If 2 were initially affected, that is your initial population. If 3 more were affected in the first week then the original 2 plus 3 more would be a total of five. Since X_n denotes the total number of affected children after n weeks then X₁ would be 5.