import matplotlib.pyplot as plt
import numpy as np

def generic_exponential(x, A, B, Gamma, beta):
    return A*(1-np.exp(-(Gamma*x)**beta))+B

x = np.logspace(-2, 2, num=200)

y1 = generic_exponential(x, 1, 0, 1, 2)
plt.semilogx(x, y1, 'b-')
plt.xlabel(r'$\Delta t$')
plt.ylabel(r'$D(\Delta t)$')
plt.show()