Please solve this math with step by step explanation

7. Suppose it is known that the population of a community is 20, 000. During the beginning of the current COVID-lQ pandemic (that is, at time t = 0 or at Day 1), it is reported that 50 people are carrying the disease (caused by SARS-CoVZ virus). The rate at which the virus spreads can be modeled by the ordinary differential equation (ODE): I' = k (at + in?) ; I (0) = 50 where I(t) denotes the number of infected individuals. Suppose the model ts very well with the rst 12 days1 infected data (see, Table 1) and therefore the parameters are estimated as: k = 0.09, a = 100, b = 1. We can apply this model to predict the number of individuals who will become infected in near future. Such projections will help the community to take the necessary measures so that the spread of the SERS-COVQ virus can be prevented or controlled. Now answer the following sub-questions: (i) At the pandemic peak, the number of infected individuals will reach to the maximum. So it's important to predict the peak time (in days). According to the model, when will the peak of the infection arise ? (ii) Find the number of individuals of the community who is likely to become infected at the pandemic peak if Ht) follows the cubic form: c1 + Cgt2 + 63:3 where c1 = 50,02 = 3 and 03 = %. (iii) Identify the appropriate time (interval) after when the infection is about to decrease. Table:1 Number of COVID- 19 infected people in the community Dayl 13:52 Days Day No. of Infected 50 54 67 89 120 158 Days Day 7 Day 8 Day 9 Day 10 Day 11 Day 12 No. of Infected 205 260 470 555