%matplotlib widget
import matplotlib.pyplot as plt
import numpy as np

fig, ax = plt.subplots()
decay = lambda C, K, x: C *(1-np.exp(-1*K*x))
x = np.linspace(0,10,10)

# Create a secondary y axis on the right
twin_ax = ax.twinx()

for n in range(5):
    C = n**2 + 5
    K = 0.75
    # Plot the exponential decay on left y axis 
    ax.plot(x,decay(C,K,x), marker='o', linestyle='--', label=C)
    # Plot the limit of decay on right y axis 
    twin_ax.axhline(y=C, color='gray') 
    
ax.legend()
ax.set_xlabel('X')
ax.set_ylabel('Measured values')
twin_ax.set_ylabel('Theoritical limit')

# Align the both left and right y axis 
twin_ax.set_ylim(ax.get_ylim())

##################
# Issues or bugs
# Need to fix the X limits or else 
# the graph doens't display properly
##################

print('xlim before fix: {}'.format(ax.get_xlim()))
ax.relim()
print('xlim after relim(): {}'.format(ax.get_xlim()))
# A hack to fix the issue # https://stackoverflow.com/a/27344398/4988010
twin_ax.plot(0, 0, visible=False)
print('xlim after fixing: {}'.format(ax.get_xlim()))

plt.show()