POW FOR EXPONENTIAL GROWTH AND DECAY

#!/usr/bin/env python3
"""
POW FOR EXPONENTIAL GROWTH AND DECAY
Population growth, radioactive decay, bacterial growth
"""

print("=== Population Growth ===")
initial_population = 1000
growth_rate = 0.03  # 3% per year
years = 20

# P(t) = P0 * (1 + r)^t
final_population = initial_population * pow(1 + growth_rate, years)
print(f"Initial: {initial_population}")
print(f"After {years} years: {final_population:.0f}")
print(f"Growth: {final_population - initial_population:.0f}")

print("\n=== Radioactive Decay (Half-Life) ===")
initial_mass = 100  # grams
half_life = 5  # years
time = 15  # years

# N(t) = N0 * (1/2)^(t/half_life)
remaining = initial_mass * pow(0.5, time / half_life)
print(f"Initial mass: {initial_mass}g")
print(f"Half-life: {half_life} years")
print(f"After {time} years: {remaining:.2f}g")
print(f"Decayed: {initial_mass - remaining:.2f}g")

print("\n=== Bacterial Growth (Doubling) ===")
initial_bacteria = 100
doubling_time = 20  # minutes
time_elapsed = 120  # minutes

# N(t) = N0 * 2^(t/doubling_time)
final_count = initial_bacteria * pow(2, time_elapsed / doubling_time)
print(f"Starting bacteria: {initial_bacteria}")
print(f"Doubles every: {doubling_time} minutes")
print(f"After {time_elapsed} minutes: {final_count:.0f}")

print("\n=== Medicine Concentration (Exponential Decay) ===")
initial_dose = 500  # mg
elimination_rate = 0.20  # 20% per hour
hours = 8

# C(t) = C0 * (1 - r)^t
remaining = initial_dose * pow(1 - elimination_rate, hours)
print(f"Initial dose: {initial_dose}mg")
print(f"After {hours} hours: {remaining:.2f}mg")
print(f"Eliminated: {initial_dose - remaining:.2f}mg")

print("\n=== Moore's Law (Transistor Doubling) ===")
transistors_2000 = 42_000_000
years_passed = 24  # 2000 to 2024
doubling_period = 2  # doubles every 2 years

transistors_2024 = transistors_2000 * pow(2, years_passed / doubling_period)
print(f"Year 2000: {transistors_2000:,} transistors")
print(f"Year 2024: {transistors_2024:,.0f} transistors")
print(f"Increase: {transistors_2024 / transistors_2000:.1f}x")