dP Suppose that the population P(t) of a country satisfies the differential equation =kP(1200-P) with k constant. Its dt population in 1960 was 300 million and was then growing at the rate of 1 million per year. Predict this country's population for the year 2030. *** This country's population in 2030 will be million. (Type an integer or decimal rounded to one decimal place as needed.)

Suppose that news spreads through a city of fixed size of 800000 people at a time rate proportional to the number of people who have not heard the news. (a.) Formulate a differential equation and initial condition for y(t), the number of people who have heard the news t days after it has happened. No one has heard the news at first, so y(0) the number of people who have heard the news is proportional to the number of = 0. The "time rate of increase in people who have not heard the news" translates into the differential equation dy k( |3D dt

A virus has already infected 4 million people in a country before a vaccine becomes available to the public. Once vaccination starts, the number of infected people decreases at a rate that is proportional to the cube of the number of infected people. One month later, there are still 2 million people that are infected. Let p be the number of infected people (in millions) and t be the number of months since vaccination has started. (a) Find a differential equation and initial conditions to model the situation. (b) Solve the differential equation to find pp as a function of t (c) How many people are still infected three months after vaccination starts?