A country's population consists of both urban and rural inhabitants. Currently the population is 45% urban and 55% rural. The total population does not change in this country, although people move between urban and rural areas as follows: • Each year 6% of the urban population migrates to the rural countryside, while the other 94% stays in the urban city. • Each year 9% of the rural population migrates to the urban cities, while the other 91% stays in the rural country. (a) Let u(t) represent the percentage of the total population that is urban as a function of time t in years. Similarly, let r(t) represent the percentage of the total population that is rural as a function of years. Write a system of differential equations modeling the rates of change in u(t) and r(t). Note: use the variables u and r in entering your answers below. Do not use u(t) and r(t). du dt dr dt == (b) What are the initial conditions? Write in decimal form. u(0) r(0) == 0.45 = 0.55 (c) Your linear system should have two distinct eigenvalues. Enter these values separated by a comma: The eigenvalues are: 0,5 (d) What is the solution to the IVP? u(t) = r(t) = (e) In the long term, the population will be 60 urban and 40 rural.