get_rate <- function(m, x_zero, r, t) {
  rate = m*x_zero * (exp(r*t) - 1) / r
  return(rate)
}
m = 0.0001
r = 0.01
x_zero = 10
times <- 1:1000
probabilities_at_least_1000 <- numeric(length = length(times))
for(t in times)
{
  prob_at_leat_1000[t] <-  ppois(q=1000,
                                 lambda = get_rate(m, x_zero, r, t=t),
                                 lower.tail = F)
}
plot(times, prob_at_leat_1000)