Visualizing cell growth
I would recommend looking into Python's plotting utilities, for example here.

I would recommend specifically looking at the examples that plot mathematical functions.

The basic idea is that you create a function that computes your equation based on the different parameters as inputs ($a, a_{max}, l_{max}$) and then you can plug in a range of values for each parameter and plot e.g. with $a_{max}$ on the x axis, then different lines showing a range of values for $l_{max}$, or whatever makes sense for you.

e.g. 

import numpy as np
import matplotlib.pyplot as plt

def fn(a, amax, lmax):
  return lmax/2 + (a/amax) * (lmax/2)

plt.figure()
amax = np.arange(0.01, 1, .01)
plt.plot(amax, fn(.005, amax, .1), "ro") ## red points
plt.plot(amax, fn(.005, amax, .2), "go") ## green point
plt.show()


I have no idea if these parameter ranges are meaningful for you, you will have to figure that out for yourself.