the population of new york city 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 morning rush hour lasts 3 hours. what would be the population if rush-hour growth rate continued for 12 hours instead of 3.
since 12 = 3*4
it would double 4 times instead of just once, right?
so, what is 2^4 ?
Well, if the population of New York City doubles during the workday, we can say that during rush hour, the population would be 8,000,000 people (or clowns, just for fun). Now, if the population decreases by half at the end of the workday, then the population after the rush hour would be 8,000,000 / 2 = 4,000,000 clowns.
If morning rush hour lasts for 3 hours, and the population doubles during that time, we can assume that the population growth rate is 8,000,000 / 3 = 2,666,666.67 new clowns per hour.
If this growth rate continues for 12 hours instead of 3, then we can calculate the population as follows:
2,666,666.67 new clowns per hour x 12 hours = 32,000,000 clowns in total.
So, the population at the end of the 12-hour rush-hour period would be approximately 32,000,000 clowns. Good luck finding that many red noses!
To find out the population after 12 hours of rush hour growth rate, we can break down the steps:
1. Morning Rush Hour:
The population doubles during rush hour, which lasts for 3 hours. So, after the morning rush hour, the population would be 4,000,000 * 2 = 8,000,000 people.
2. Workday Population:
After the morning rush hour, the population remains the same until the end of the workday. So, the population would still be 8,000,000 people.
3. End of the Workday:
At the end of the workday, the population decreases by half. Therefore, the population would be 8,000,000 / 2 = 4,000,000 people.
4. Evening Rush Hour:
Since we want to calculate the population after 12 hours of rush hour growth rate, we need to find out how many additional rush hours are included.
12 hours total - 3 hours morning rush hour = 9 additional hours of rush hour.
During each hour of rush hour, the population doubles. So after 12 hours, the population would be multiplied by 2 for each of the 9 additional rush hours.
Final Population Calculation:
4,000,000 * (2^9) = 4,000,000 * 512 = 2,048,000,000 people.
Therefore, the population of New York City would be approximately 2,048,000,000 people if the rush hour growth rate continued for 12 hours instead of 3.
To calculate the population if the rush-hour growth rate continued for 12 hours instead of 3, you need to follow these steps:
Step 1: Determine the population during the morning rush hour
Since the population doubles during the workday, the population at the end of the morning rush hour would be 4,000,000 * 2 = 8,000,000 people.
Step 2: Calculate the population decrease after the morning rush hour
The population decreases by half at the end of the workday, so the population after the morning rush hour would be 8,000,000 / 2 = 4,000,000.
Step 3: Calculate the growth rate per hour
To find the growth rate per hour during rush hour, divide the population increase during rush hour by the duration of rush hour: (8,000,000 - 4,000,000) / 3 = 4,000,000 / 3 = 1,333,333 people per hour.
Step 4: Calculate the population after 12 hours of rush-hour growth rate
To find the population after 12 hours of rush-hour growth rate, multiply the growth rate per hour by the number of hours: 1,333,333 * 12 = 15,999,996.
Therefore, if the rush-hour growth rate continued for 12 hours instead of 3, the population of New York City would be approximately 15,999,996 people.