# -*- coding: utf-8 -*-
"""
Created on Wed Feb 04 12:13:53 2015

Listing 15.2 : décroissance d'une population de 
noyaux radioactifs

@author: grivet
"""
import numpy as np
import matplotlib.pyplot as plt

N = 1000; P = 0.1
NR = 40;
nB = np.zeros(NR)
tab = np.zeros(N) 
nB[0] = sum(tab) 
for ir in range(1,NR):
    for i in range(N):
        x = np.random.rand()
        if x <= P and tab[i] == 0:
            tab[i] = 1
    nB[ir] = sum(tab)
nA = N-nB
t = np.array(range(NR))
plt.xlabel("nombre de balayages")
plt.ylabel("populations")
plt.plot(t,nA,'ob',t,nB,'or')
plt.plot(t,N*exp(-P*t),'-k')