import matplotlib.pyplot as plt
def pow_int(base, exponent, current):
    if exponent < 1:
        return current
    return pow_int(base, exponent -1, int(current*base))

def pow_float(base, exponent, current):
    if exponent < 1:
        return current
    return pow_float(base, exponent -1, current*base)

start = 50
base = 1.03
idx = []
ival, fval = [], []
for i in range(100):
    idx.append(i)
    fval.append(pow_float(base, i, start))
    ival.append(pow_int(base, i, start))


plt.figure(figsize=(10, 8))
plt.plot(idx, ival, 'bx-', label='int')
plt.plot(idx, fval, 'gx-', label='float')
    
plt.xlabel('idx')
plt.ylabel('power')
plt.title('Clustering Scores vs. Number of Clusters')
plt.legend()
plt.show()