Answer Happy

Consider a population in a controlled environment (no predators, no epidemics, no shortage of food supplies, unlimited space, no migration). If we suppose that the number of individuals N changes in the time interval At only due to births and deaths, then N(t + At) = N(t) + n. births - n. deaths (1) 1. Now suppose that the number of births and deaths are proportional to the number of individuals. In such a case, both the birth rate per unit time and the death rate per unit time are constant, and consequently, the growth rate per unit time R is as well. Write the mathematical model so that the birth and death terms are written in terms of R and N(t) only. Find the solution of such an equation (used the procedure we used in class on Thursday, August 26, 2021 - see Solutions on iLearn, to solve difference equations). If the initial population at time t = to is N(to) = No, plot the solution on Desmos in the following four cases (include each graph in your pdf with the corresponding value of RAT): (a) RAt > 0; (b) -1