import numpy as np
import matplotlib.pyplot as plt

hours = [0, 6, 12, 18, 24]
cell_numbers = [10, 20, 2000, 3200, 3500]

# Fit a polynomial of degree 2 (quadratic)
coefficients = np.polyfit(hours, cell_numbers, 2)
polynomial = np.poly1d(coefficients)

# Create a smoother range of hours
hours_new = np.linspace(min(hours), max(hours), 300)
cell_numbers_smooth = polynomial(hours_new)

plt.figure(figsize=(10, 6))
plt.plot(hours_new, cell_numbers_smooth, color='b', label='Polynomial Fit')
plt.scatter(hours, cell_numbers, color='red', label='Data Points')

plt.title('Cell Number Over Time')
plt.xlabel('Hour')
plt.ylabel('Cell Number')
plt.grid(True)
plt.legend()
plt.show()