Take sample from diminishing population - r

Question

I would like to take a random sample of rows from a data.frame, apply a function to the subset, then take a sample from the remaining rows, apply the function to the new subset (with different parameters), and so on.
A simple example would be if 5% of a population dies each month, in month 2 I need the population minus those ones who died in time month 1.
I have put together a very verbose method of doing this involving where I save the IDs from the sampled rows, then subset them out from the data for the second period, etc.
library(data.table)
dt <- data.table(Number=1:100, ID=paste0("A", 1:100))
first<-dt[sample(nrow(dt), nrow(dt)*.05)]$ID
mean(dt[ID %in% first]$Number)
second<-dt[!(ID %in% first)][sample(nrow(dt[!(ID %in% first)]),
nrow(dt[!(ID %in% first)])*.05)]$ID
mean(dt[ID %in% c(first,second)]$Number)
dt[!(ID %in% first)][!(ID %in% second)] #...
Obviously, this is not sustainable past a couple periods. What is the better way to do this? I imagine this is a standard method but couldn't think what to look for specifically. Thanks for any and all input.

Answer 1

This shows how to "grow" a vector of items that have been sampled at a 5% per interval time course:
removed <- numeric(0)
for ( i in 1:10){
removed <- c(removed, sample( (1:100)[!(1:100) %in% removed], # items out so far
(100-length(removed))*.05)) # 5% of remainder
cat(c(removed, "\n")) # print to console with each iteration.
}
54 1 76 96 93
54 1 76 96 93 81 16 13 79
54 1 76 96 93 81 16 13 79 80 74 30 29
54 1 76 96 93 81 16 13 79 80 74 30 29 52 33 86 19
54 1 76 96 93 81 16 13 79 80 74 30 29 52 33 86 19 34 32 41 62
54 1 76 96 93 81 16 13 79 80 74 30 29 52 33 86 19 34 32 41 62 5 70 8
54 1 76 96 93 81 16 13 79 80 74 30 29 52 33 86 19 34 32 41 62 5 70 8 66 82 50
54 1 76 96 93 81 16 13 79 80 74 30 29 52 33 86 19 34 32 41 62 5 70 8 66 82 50 6 91 99
54 1 76 96 93 81 16 13 79 80 74 30 29 52 33 86 19 34 32 41 62 5 70 8 66 82 50 6 91 99 46 27 51
54 1 76 96 93 81 16 13 79 80 74 30 29 52 33 86 19 34 32 41 62 5 70 8 66 82 50 6 91 99 46 27 51 22 23 20
Notice that the actual number of items added to the list of "removals" will be decreasing.