One model for the spread of a virusis that the rate of spread is proportional to the product of the fraction of the population P who have contracted the virusand the fraction who have not contracted the virus. a.Write out a differential equation that is satisfied by P. b.Solve the differential equation. c.Ina small communityof 100,000 inhabitants. At 8:00 am on the initial day of reporting, 100peoplehad contractedthe virus. By 8:00 am on the third day,200more people had contacted the virus. At what time will 90% of the population havecontracted the virus