import matplotlib.pyplot as plt
import numpy as np
from math import exp

def get_x(T, x0, h, a):
    all_x = [x0]
    x_prior = x0
    for i in range(0, int(T/h)):
        x = x_prior + x_prior*h*a
        all_x.append(x)
        x_prior = x
    return all_x

def get_x_2(T, x0, a, h, time):
    all_x = [x0]
    x_prior = x0
    for i in range(0, int(T/h)):
        x = x_prior * exp(a*time[i])
        all_x.append(x)
        x_prior = x
    return all_x

def get_x_4(T, x0, a, h):
    all_x = [x0]
    x_prior = x0
    for i in range(0, int(T / h)):
        x = x_prior * exp(a * i)
        all_x.append(x)
        x_prior = x
    return all_x

#print(get_x_3(13,0.2))

fig = plt.figure()

T, x0, t0, h, a1, a2 = 13, 1, 0, 0.8, 1, -1

y = np.arange(t0, T, h).tolist()

x1 = get_x(T, x0, h, a1)
x2 = get_x(T, x0, h, a2)
x3 = get_x_2(T, x0, a1, h, y)
x4 = get_x_2(T, x0, a2, h, y)
x41 = get_x_4(T, x0, a2, h)
print(x4)
print(x41)

ax1 = fig.add_subplot(211)
ax1.plot(y,x1)
ax1.plot(y,x3,'1')

ax2 = fig.add_subplot(212)
ax2.plot(y,x2)
ax2.plot(y,x4,'1')

plt.show()