Consider the following model for a population that is changing due to births, deaths, immigration, and emigration. Suppose the population at time t is y, k(t) = birth rate minus death rate (in daily births/deaths per thousand people), and m(t) = immigration rate minus emigration rate (in people per day). a) Write down the differential equation that describes the rate dy/dt of change of the population. Write the equation in the form dy/dt = _____________________. Hint: You should have a linear ordinary differential equation of order one and degree one.

b). Suppose m and k are constants. Find an explicit formula for the solution. For four different values of m and k, plot the solutions. Choose the combinations of m and k different physical solutions. Interpret the solutions.