import numpy as np
import matplotlib.pyplot as plt
 
L = np.array([
    [0, 1, 1.8, 1.7, 0],
    [0.61, 0, 0, 0, 0],
    [0, 0.29, 0, 0, 0],
    [0, 0, 0, 0.19, 0],
    [0, 0, 0, 0.13, 0.08]
])
L = np.linalg.inv(L)
population_vector = np.array([289, 211, 120, 76, 51])
 
populations = [population_vector]
for _ in range(2):
    population_vector = L @ population_vector
    populations.append(population_vector)
 
years = range(0, -5, -2)
populations = np.array(populations).T
for age_group, pop in enumerate(populations):
    plt.plot(years, pop, label=f'Age group {age_group}')
plt.legend()
plt.xlabel('Years')
plt.ylabel('Population')
plt.title('Backwards Cod Population Projections')
plt.show()

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