def compute_sick(n):
    # computes total sick after n days
    total_sick = 1
    newly_sick = 1
    for day in range(2, n + 1):
        # each iteration represents one day
        newly_sick = newly_sick * 2
        total_sick = total_sick + newly_sick
    return total_sick

def time_to_catastrophe(population):
    days = 1
    newly_sick = 1
    total_sick = 1
    while total_sick < population:
        newly_sick = newly_sick * 2
        total_sick = total_sick + newly_sick
        days = days + 1
    print(days, "days for the entire population to get sick")
    return(days)