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 Covid19 but have recovered or who have passed before dayt Many communities are interested in A(t) A(t), the number of people infected on day t-1 t1. 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 Mt) related? Write an equation connecting these three quantities and explain why this is true c.) What is the meaning of N(t1) 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)