import matplotlib.pyplot as plt
import numpy as np

# Initial population at year 1
initial_population = 1_000_000
death_rate = 0.10

# Start and stop years for the graph
start_year = 4000
stop_year = 10000
interval = 500  # Interval for plotting data points

# Calculate the population at the start of the start_year
current_population = initial_population
for _ in range(start_year // 100):  # Dividing by 100 as the death rate is applied every 100 years
    current_population -= death_rate * current_population

# Now calculate and plot the population from start_year to stop_year
years = np.arange(start_year, stop_year + 1, interval)
population_values = []
for year in years:
    # Apply the death rate for each interval (interval/100 times for each period)
    for _ in range(interval // 100):
        current_population -= death_rate * current_population
    population_values.append(current_population)

# Create the graph with labels for each data point
plt.figure(figsize=(8, 6))
plt.plot(years, population_values, marker='o', linestyle='-', color='b')
plt.xlabel('Years')
plt.ylabel('Population')
plt.title(f'Population Projection from Year {start_year} to {stop_year}')

# Adding labels to the data points
for i, txt in enumerate(population_values):
    plt.annotate(f"{int(txt):,}", (years[i], population_values[i]), textcoords="offset points", xytext=(0,10), ha='center')

plt.grid(True)
plt.show()