Suppose COVID-19, a pandemic that spread worldwide has infected 40,000 people on August 2020. Each day, the number of infected is estimated to be 300. Assuming that the number of daily infections are...

Suppose COVID-19, a pandemic that spread worldwide has infected 40,000 people on August 2020. Each day, the number of infected is estimated to be 300. Assuming that the number of daily infections are constant,

1. What is the monthly growth rate of infection k? Assume time t is measured in months.

2. How many persons will be confirmed positive by the end of December 2020?

3. Assuming that there has a turn of events and a vaccine is discovered by September 2020. In addition, the number of cases dropped with the number of recoveries at a rate of 100 per day. There have been no additional cases after September. How much time t will elapse for the cases of COVID-19 to drop to 500?