rm(list=ls())

p <- .15 # fraction of cells that survive each reproduction

#Define vector n(t):  number of cells per generation
generation_end=20;  #predict up to this generation in the future

n <- vector()
n[1] <- 1000 # initial number of cells

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

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