The population of New York doubles during the workday. At the end of the workday, the population decreases by half. If the population in New York City is roughly 4,000,000 people before rush hour, and the morning rush hour lasts 3 hours, what would be the population if the rush-hour growth rate continued for 12 hours instead of 3? People leave the city for home at the same rate as they come into the city. What would be the population if the decay rate continued for 12 hours at the end of the day when everyone gets home?
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To find the population if the rush-hour growth rate continued for 12 hours instead of 3, we need to apply the doubling rate for each hour.
Since the population doubles during the workday and the morning rush hour lasts for 3 hours, we can calculate the population at the end of the rush hour as follows:
Population after the morning rush hour = 4,000,000 * 2^3
= 4,000,000 * 8
= 32,000,000
So if the morning rush hour lasts for 3 hours, the population increases to 32,000,000.
Now, to find the population if the rush-hour growth rate continues for 12 hours, we need to apply the doubling rate for each hour:
Population after 12 hours of rush hour = 4,000,000 * 2^12
= 4,000,000 * 4096
= 16,384,000,000
Therefore, if the growth rate continued for 12 hours, the population would be approximately 16,384,000,000.
Now, let's calculate the population when the decay rate continues for 12 hours at the end of the day when everyone gets home.
Given that the population decreases by half at the end of the workday, we can apply the halving rate for each hour:
Population after 12 hours of decay = 4,000,000 / 2^12
= 4,000,000 / 4096
= 976.5625
Therefore, if the decay rate continued for 12 hours, the population would be approximately 976.5625.
Please note that these calculations assume a constant growth and decay rate, which may not accurately represent real-world population dynamics.