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.

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The rate of change is 0.08 billion per year.

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