<jupyter_start><jupyter_text><jupyter_code>import numpy as np
k=np.log(19999/((20000/345)-1))/50
def c(t):
  return 20000 / (1+19999 * np.exp(-k*t))  
t = np.arange(0,175,0.01)
c(t)
dcdt=k*c(t)*(1-(c(t)/20000))
 import matplotlib.pyplot as plt
 plt.figure(figsize=(18,10))
 plt.plot(t, c(t),c="red",linestyle="--")
 plt.axvline(np.log(19999)/k)
plt.plot(c(t),dcdt)
plt.axhline(590, linestyle="--")<jupyter_output><empty_output>