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4.) Oh no! 12 zombies started attacking people in Philadelphia. Within a week, there were 1536 zombies.

A. On average, how many people did each zombie zombify each day?

B. How many zombies would there be in 16 days?

C. Philadelphia's population is about 1.6 million. How many days would it take to infect the entire city?

Answer :

Final answer:

The average new zombification rate is approximately 217.71 zombies per day. In 16 days under similar exponential growth, the zombie count could reach around 2.77 million. To infect the entire city of Philadelphia, it would take approximately 14 days, given the rapid spread.


Explanation:

Zombies in Philadelphia!


A student poses an interesting hypothetical question about zombies in Philadelphia. We have the following information to work with:



  • Initially, there were 12 zombies.

  • After one week (7 days), the zombie population grew to 1536.



A. Average zombification rate per day


To find out how many people each zombie turned into zombies, we first need to calculate how many zombies were created in total:



  2. Final Zombie Count = 1536

  4. Initial Zombie Count = 12

  6. New Zombies Created = Final Zombie Count - Initial Zombie Count = 1536 - 12 = 1524


Assuming the growth is uniform over 7 days, the average number of new zombies created per day is:



  2. Average New Zombies per Day = New Zombies Created / 7 = 1524 / 7 ≈ 217.71


If we consider that each zombie infects one person every day, on average:



  2. Average Zombification Rate = Average New Zombies per Day = ≈ 217.71



B. Predicting Zombie Growth over 16 Days


If the current growth pattern continues, we can project how many zombies there would be in 16 days. Let's assume the growth is exponential and follows the same rate established in the first week.



  2. In one week (7 days) we reached 1536 zombies.

  4. Therefore, the growth factor for 1 day = 1536 / 12 = 128. The increase factor is achieved every day.

  6. In 16 days, using a simplified exponential model:
    Number of Zombies = Initial Number (Growth Rate)^(days)
    = 12     (128)^(16/7) = 12 * (128)^(2.285714) = approx. 2.77 million zombies.



C. Time to Infect Philadelphia


To determine how many days it would take to infect the entire population of Philadelphia, which is about 1.6 million people:



  2. In the first week, we have around 1536 zombies. Assuming exponential growth, we have:

  4. From day 7 to day 14, we multiply again by a growth factor of 128, so by day 14 we would surpass 1.6 million significantly.

  6. In practical terms, since exponential growth accelerates quickly, we can estimate that it would take about 14 days to reach well beyond 1.6 million.



Learn more about Zombie infection spread here:

https://brainly.com/question/29643450


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