Generate random numbers from exponential distribution and model using python

My goal is to create a dataset of random numbers that looks like an exponential decay function and then plot an exponential decay function through those points.

First I tried to create a series of random numbers from an exponential distribution.

from pylab import *
from scipy.optimize import curve_fit
import random
import numpy as np
import pandas as pd

testx = pd.DataFrame(range(10)).astype(float)
testx = testx[0]

for i in range(1,11):
   x = random.expovariate(15) # rate = 15 arrivals per second
   data[i] = [x]

testy = pd.DataFrame(data).T.astype(float)
testy = testy[0]; testy

plot(testx, testy, 'ko')

The result could look something like this (but note, I need this to look like an exponential decay function always).

And then I define a function to draw a line through my points:

def func(x, a, e):
return a*np.exp(-a*x)+e

popt, pcov = curve_fit(f=func, xdata=testx, ydata=testy, p0 = None, sigma = None) 

print popt # parameters
print pcov # covariance

plot(testx, testy, 'ko')

xx = np.linspace(0, 15, 1000)
plot(xx, func(xx,*popt))

plt.show()

What I'm looking for is: (1) a more elegant way to create an array of random numbers from an exponential (decay) distribution and (2) how to test that my function is indeed going through the data points.