rm(list=ls())

p <- .95 # fraction of cells that survive each reproduction

#Define vector n(t):  number of cells per generation
generation_end=100;  #predict up to this generation in the future
K=2000;   #reproduction capacity

n <- vector()
n[1] = 1000; #initial number of cells (generation 0)

for (t in 2:generation_end)
  n[t] <- 4*n[t-1]*p*(1-n[t-1]/K)

plot(1:generation_end, n, type = "b", xlab = "t", ylab = "n(t)",
     main = expression(4*n[t-1]*p*(1-n[t-1]/K)))