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John Hopkins University (JHU) reports Covid-19 statistics daily for every US state and many countries in the world. In this problem we are concerned with four of them for some region, say Arizona. Each one is a function of time t, in days. P(t) - Cumulative Confirmed Cases: total number of cases confirmed before day t N(t) - Daily New Cases: number of cases first confirmed on day t R(t) - Cumulative Recovered or Removed: total number of people who were confirmed to have Covid-19 but have recovered or who have passed before day t Many communities are interested in A(t) A(t), the number of people infected on day t-1 t-1. This is important because it gives the community an idea of the hospital capacity they may need. a.) What is the meaning of P(t+1)? Answer in words. b.) How are P(t+1) and P(t) and N(t) related? Write an equation connecting these three quantities and explain why this is true c.) What is the meaning of N(t-1) and N(t-2)? Answer in words. d.) How can you find A(t) from P(t) and one of the other two functions, N and R? Use this to write a formula for A(t). (For this problem, assume no one is infectious the day they get diagnosed.) Then explain e.) Use the fact that most Covid cases last for two weeks (14 days) and assume that people are infectious for the whole 14 days. Write a formula for A(t) in terms of the function N (and no other functions).

John Hopkins University (JHU) reports Covid-19 statistics daily for every US state and many countries in the world. In this problem we are concerned with four of them for some region, say Arizona. Each one is a function of time t, in days. P(t) - Cumulative Confirmed Cases: total number of cases confirmed before day t N(t) - Daily New Cases: number of cases first confirmed on day t R(t) - Cumulative Recovered or Removed: total number of people who were confirmed to have Covid-19 but have recovered or who have passed before day t Many communities are interested in A(t) A(t), the number of people infected on day t-1 t-1. This is important because it gives the community an idea of the hospital capacity they may need. a.) What is the meaning of P(t+1)? Answer in words. b.) How are P(t+1) and P(t) and N(t) related? Write an equation connecting these three quantities and explain why this is true c.) What is the meaning of N(t-1) and N(t-2)? Answer in words. d.) How can you find A(t) from P(t) and one of the other two functions, N and R? Use this to write a formula for A(t). (For this problem, assume no one is infectious the day they get diagnosed.) Then explain e.) Use the fact that most Covid cases last for two weeks (14 days) and assume that people are infectious for the whole 14 days. Write a formula for A(t) in terms of the function N (and no other functions).

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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John Hopkins University (JHU) reports Covid-19 statistics daily for every US state and many countries in the world. In this problem we are concerned with four of them for some region, say Arizona. Each one is a function of time t, in days. P(t) - Cumulative Confirmed Cases: total number of cases confirmed before day t N(t) - Daily New Cases: number of cases first confirmed on day t R(t) - Cumulative Recovered or Removed: total number of people who were confirmed to have Covid-19 but have recovered or who have passed before day t Many communities are interested in A(t) A(t), the number of people infected on day t-1 t-1. This is important because it gives the community an idea of the hospital capacity they may need. a.) What is the meaning of P(t+1)? Answer in words. b.) How are P(t+1) and P(t) and N(t) related? Write an equation connecting these three quantities and explain why this is true c.) What is the meaning of N(t-1) and N(t-2)? Answer in words. d.) How can you find A(t) from P(t) and one of the other two functions, N and R? Use this to write a formula for A(t). (For this problem, assume no one is infe tious the day they get diagnosed.) Then explain e.) Use the fact that most Covid cases last for two weeks (14 days) and assume that people are infectious for the whole 14 days. Write a formula for A(t) in terms of the function N (and no other functions).
Transcribed Image Text:John Hopkins University (JHU) reports Covid-19 statistics daily for every US state and many countries in the world. In this problem we are concerned with four of them for some region, say Arizona. Each one is a function of time t, in days. P(t) - Cumulative Confirmed Cases: total number of cases confirmed before day t N(t) - Daily New Cases: number of cases first confirmed on day t R(t) - Cumulative Recovered or Removed: total number of people who were confirmed to have Covid-19 but have recovered or who have passed before day t Many communities are interested in A(t) A(t), the number of people infected on day t-1 t-1. This is important because it gives the community an idea of the hospital capacity they may need. a.) What is the meaning of P(t+1)? Answer in words. b.) How are P(t+1) and P(t) and N(t) related? Write an equation connecting these three quantities and explain why this is true c.) What is the meaning of N(t-1) and N(t-2)? Answer in words. d.) How can you find A(t) from P(t) and one of the other two functions, N and R? Use this to write a formula for A(t). (For this problem, assume no one is infe tious the day they get diagnosed.) Then explain e.) Use the fact that most Covid cases last for two weeks (14 days) and assume that people are infectious for the whole 14 days. Write a formula for A(t) in terms of the function N (and no other functions).
Expert Solution
Step 1

Given,

P(t) - Cumulative Confirmed Cases: total number of cases confirmed before day t

 

N(t) - Daily New Cases: number of cases first confirmed on day t

 

R(t) - Cumulative Recovered or Removed: total number of people who were confirmed to have Covid-19 but have recovered or who have passed before day t

 

A(t) is the number of people infected on day t-1

 

Where t is the time in days.

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