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Question 3.] (10 marks) A city experiences outbreaks of two variants of a virus. The Delta variant outbreak begins with 4 peo ple infected and grows exponentially so that every week the number of people infected is 1.5 times the number the week before. The Omicron variant outbreak begins exactly 2 weeks after the Delta variant outbreak with 3 people infected and grows exponentially so that every week the number of people in- fected doubles. This continues for 8 weeks after the rst Delta infection. (For the purposes of our model we allow the number of people infected to take non-integer values.) a) How many people have each of the variants 8 weeks after the rst Delta variant infection? b) The city institutes a lockdown exactly 8 weeks after the rst Delta infection. During the lockdown the number of Omicron cases decreases exponentially so that every week the number of people infected is g times the number the week before. How long must the lockdown last before the Omicron variant is eliminated (assume this happens when the number of infected people reaches 1). c) At some point before the lockdown the number of people infected by each variant was equal. Exactly how long from the rst Delta infection did this occur