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The population of the world was about 5.3 billion in 1990 (t = 0) and about...

The population of the world was about 5.3 billion in 1990 (t = 0) and about 6.1 billion in 2000 (t = 10). Assuming that the carrying capacity for the world population is 50 billion, the logistic differential equation

dP =kP(50−P)dt

models the population of the world P(t) (measured in billions), where t is the number of years after 1990. Solve this differential equation for P(t) and use this solution to predict what the population will be in 2050 according to this model.

The population of the world was about 5.3 billion in 1990 (t = 0) and about 6.1 billion in 2000 (t = 10). Assuming that the carrying capacity for the world population is 50 billion, the logistic differential equation

dP =kP(50−P)dt

models the population of the world P(t) (measured in billions), where t is the number of years after 1990. Solve this differential equation for P(t) and use this solution to predict what the population will be in 2050 according to this model.

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