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mariomintchev
6. Another model for population growth is the logistic model. This model assumes that there is a maximum population, also known as a carrying capacity, and that the rate of population growth slows as the population approaches the carrying capacity. The variables for a logistic model are deﬁned below. • t - time, the number of years since July 1, 1965 • P(t) - the population at time t in billions of people • P0 - the population at time t = 0 in billions of people • M - the maximum population or carrying capacity in billions of people • k - a constant The logistic model for population growth is given by: P(t) =MP0 / P0 + (M − P0)e^−kt The human carrying capacity of the earth is a very controversial subject. According to Joel E. Cohen, estimates for the human carrying capacity of the earth have ranged from less than 1 billion to more than 1 trillion people. Cohen states,”Such estimates deserve the same profound skepticism as population projections” [1]. With the understanding that estimates for human carrying capacity warrant skepticism, let us consider the implications of a carrying capacity of 12 billion people. (Cohen calculated the median of 65 upper bounds on human carrying capacity to be 12 billion people [1].) Assuming that the human carrying capacity of the earth is 12 billion people, ﬁnd a logistic model for the world population using the data that you found in question 2.
Question 2) The world population on July 1, 1965 was 3.3 billion. On July 1, 1970 the population increased to 3.7 billion.
The rate of change is 0.08 billion per year.
Those are my answers to question 2 not the actual question. I gave them to you to help solve question 6 (this question).
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Looks like a type of differential equation problems. dy/dy=ky where k is a constant.