Question

The population of a city doubles during the workday. At the end of the workday, the population decreases

by half. If the population of the city is roughly 4,000,000 people before "rush hour," and the morning rush
hour actually lasts 3 hours, what would be the population 12 hours after the start of rush hour if the
population continued to double every 3 hours? People leave the city for home at the same rate as they
come into the city. If there are 8,000,000 people in the city during the workday, what would be the
population 12 hours after the start of the evening rush hour, which lasts 3 hours, if the population continued
to be cut in half every 3 hours?

Answer 1

The population 12 hours after the start of rush hour, which lasts 3 hours and the population doubles every 3 hours, would be 64,000,000 people. The population 12 hours after the start of the evening rush hour, which lasts 3 hours and the population is cut in half every 3 hours, would be 500,000 people.

Step-by-step explanation:

To calculate the population 12 hours after the start of rush hour, which lasts 3 hours, we need to find the number of doubling periods that occur within that time frame. Since the population doubles every 3 hours, there are 12/3 = 4 doubling periods.

Each doubling period results in the population doubling, so if the population starts at 4,000,000 people, after 4 doubling periods it would be 4,000,000 × 2⁴ = 64,000,000 people.

To calculate the population 12 hours after the start of the evening rush hour, which lasts 3 hours and the population is cut in half every 3 hours, we need to find the number of halving periods that occur within that time frame. Since the population is cut in half every 3 hours, there are 12/3 = 4 halving periods.

Each halving period results in the population being cut in half, so if the population starts at 8,000,000 people, after 4 halving periods it would be 8,000,000 × (1/2)⁴ = 500,000 people.

Answer 2

The city for home is double the run rush periods of time