Download Overall Growth Rate

Notes 8C – Real Population Growth
Example 1 Varying Growth Rate
The average annual growth rate for world population since 1650 has been about 0.7%. However, the annual
rate has varied significantly. It peaked at about 2.1% during the 1960’s and is currently (as of 2009) about
1.2%. Find the approximate doubling time for each of these growth rates. Use each to predict world population
in 2050, based on a 2009 population of 6.8 billion.
Now try Exercises 13-16.
Overall Growth Rate
The world population growth rate is the difference between the birth rate and the death rate.
growth rate = birth rate – death rate
Example 2 Birth and Death Rates
In 1950, the world birth rate was 3.7 births per 100 people and the world death rate was 2.0 deaths per 100
people. By 1975, the birth rate had fallen to 2.8 births per 100 people and the death rate to 1.1 deaths per 100
people. Contrast the growth rates in 1950 and 1975.
Now try Exercises 17-20.
Carrying Capacity – is the maximum sustainable population for any particular species in a given environment.
That is, it is the largest population the environment can support for extended periods of time.
Logistic Growth – is exponential with a fractional growth rate close to the base growth rate r when the
population is small relative to the carrying capacity. As the population approaches the carrying capacity, the
logistic growth rate approaches zero. The logistic growth rate at any particular time depends on the population
at that time, the carrying capacity, and the base growth rate r:


population

logistic growth rate  r  1 
 carrying capacity 
Figure 8.4 contrasts logistic and exponential growth for the same base growth rate r. In the exponential case,
the growth rate stays equal to r at all times. In the logistic case, the growth rate starts out equal to r, so the
logistic curve and the exponential curve look the same at early times. As time progresses, the logistic growth
rate becomes ever smaller than r, and it finally reaches zero as the population levels out at the carrying capacity.
Example 3 Logistic Growth
Consider a population that begins growing exponentially at a base rate of 5.0% per year and then follows a
logistic growth pattern. If the carrying capacity is 45 million, find the actual growth rate when the population is
20 billion.
Now try Exercises 21-22.
Example 4 Are We Growing Logistically?
Assume that the Earth’s carrying capacity is 12 billion people. Given that the population growth rate peaked in
the 1960s at about 2.1%, when the population was about 3 billion, is it reasonable to assume that human
population has been following a logistic growth pattern since the 1960s? Is it reasonable to assume that
population has been growing logistically throughout the past century? Explain?