An epidemic: One model for the spread of epidemics gives the number of newly infected individuals t days after the outbreak of the epidemic as Here n is the total number of people we expect to be...

An epidemic: One model for the spread of epidemics gives the number of newly infected individuals t days after the outbreak of the epidemic as

Here n is the total number of people we expect to be infected over the course of the epidemic, and β depends on the nature of the infection as well as on other environmental factors. For a certain epidemic, the number of new cases is

a. Make a graph of the number of new cases versus days since the outbreak. Include times up to 30 days.

b. What is the greatest number of new cases we expect to see in 1 day, and when does that occur?

c. The local medical facilities can handle no more than 25 new cases per day. During what time period will it be necessary to recruit help from outside sources?