Calculate expected number of survivors over time with a known death rate

Question

With a total number of N, a daily death rate: p1. I would like to calculate the number of survivors after certain days.

day1 : N - N*p1 
day2 : (N - N*p1) -  (N - N*p1)*p1
day3 : ((N - N*p1) -  (N - N*p1)*p1) - ((N - N*p1) -  (N - N*p1)*p1)*p1
...

This is what I have done so far to start to get the number of day 1. Suggestions would be appreciated.

df <- data.frame(day = c(1:30))  
N <- 1000
p1 <- 0.06
apply(df,1, function(x) N-N*p1) 

Answer 1

Basically, you can use the compound interest equation.

foo = function(N, p1, d){
    for (i in 1:d){
        N = N - N * p1
    }
    N
}

foo(1000, 0.06, 30)

OR

bar = function(N, p1, d){
    N * (1 - p1)^d
}

bar(1000, 0.06, 1:30)

OR if you just want a plot

curve(1000 * (1 - 0.06) ^ x, 0, 30, n = 31)