Question

A country's population consists of both urban and rural inhabitants. Currently the population is 25% urban and 75% rural. The total population does not change in this country, although people move between urban and rural areas as follows: • Each year 7% of the urban population migrates to the rural countryside, while the other 93% 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. Let u = u(t) represent the percentage of the total population that is urban as a function of time t in years. Similarly, let r = r(t) represent the percentage of the total population that is rural as a function of years. (a) What are the initial conditions? Write your answers as decimals u(0) = r(0) = (b) Select the correct system of differential equations modeling the rates of change in u(t) and r(t). { u' = - 0.07u + 0.09r { r' = 0.07u - 0.09r { u' = 0.07u - 0.09r { r' = - 0.07u + 0.09r { u' = - 0.07u { r' = 0.09r { u' = 0.25u { r' = - 0.75r

          A country's population consists of both urban and rural inhabitants. Currently the population is 25% urban and 75% rural. The total population does not change in this country, although people move between urban and rural areas as follows:

• Each year 7% of the urban population migrates to the rural countryside, while the other 93% 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.

Let u = u(t) represent the percentage of the total population that is urban as a function of time t in years. Similarly, let r = r(t) represent the percentage of the total population that is rural as a function of years.

(a) What are the initial conditions? Write your answers as decimals
u(0) =
r(0) =

(b) Select the correct system of differential equations modeling the rates of change in u(t) and r(t).

{ u' = - 0.07u + 0.09r
{ r' = 0.07u - 0.09r

{ u' = 0.07u - 0.09r
{ r' = - 0.07u + 0.09r

{ u' = - 0.07u
{ r' = 0.09r

{ u' = 0.25u
{ r' = - 0.75r

A country's population consists of both urban and rural inhabitants. Currently the population is 25% urban and 75% rural. The total population does not change in this country, although people move between urban and rural areas as follows:

• Each year 7% of the urban population migrates to the rural countryside, while the other 93% 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.

Let u = u(t) represent the percentage of the total population that is urban as a function of time t in years. Similarly, let r = r(t) represent the percentage of the total population that is rural as a function of years.

(a) What are the initial conditions? Write your answers as decimals
u(0) =
r(0) =

(b) Select the correct system of differential equations modeling the rates of change in u(t) and r(t).

u' = - 0.07u + 0.09r
r' = 0.07u - 0.09r

u' = 0.07u - 0.09r
r' = - 0.07u + 0.09r

u' = - 0.07u
r' = 0.09r

u' = 0.25u
r' = - 0.75r

Added by Magdalena H.

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