#!/usr/bin/env python
# -*- coding: utf-8 -*-

# Created on Aug 20, 2014 23:23

import math

# classic logistic function

def lf(t,k,p0,r):
  return (k*p0*math.exp(r*t))/(k+p0*(math.exp(r*t)-1))

# modified logistic function with non-renewable term
  
k = 100  # renewable carrying capacity
kn = 0   # nonrenewable carrying capacity
nr = .04 # nonrenewable rate of consumption
p0 = 1   # initial population
p = p0

maxv = 10000000 # iterations

r = 10.0/maxv  # population growth rate per period

v = []

for t in range(0,maxv+1):
    p *= 1 + r * (kn+k-p)/k
    kn = max(kn-p * nr,0)
    lp = lf(t,k,p0,r)
    v.append((p,lp))

# title line
s = '%8s %12s' % ('t','|1-a/b|')
print(s)
print('-' * len(s))

# data display    
for t,(a,b) in enumerate(v):
  if(t % (maxv/10) == 0):
    print('%8d %12.8f' % (t,abs(1-a/b)))