Human Population GrowthIntroduction

BackgroundThe human population was relatively small until only a few centuries ago. Then, as breakthroughs in medicine, agriculture, and technology were made, the death rate fell markedly (especially among children) and the population began to rise rapidly. At present, the human population is growing exponentially, and is approaching 6 billion. Such growth is causing serious problems in resource distribution, health, waste disposal, and living space.

GoalsIn this investigation you will examine and graph human population data. You will then estimate population sizes that would result given different average family sizes. You will also infer consequences of unlimited population growth.

Lab Warmup

ConceptsThe following mathematical equation can be used to project changes in populations that are increasing at an exponential rate, such as with humans.

N(t) = N(0)ert

N(t) is the population size after the passage of t units of time. The letter t stands for the number of generations, where one generation is often assumed to be about 25 years long. N(0) is the initial population size, r is the exponential growth rate, and e is a natural logarithmic constant that has a value of about 2.72. The quantity er is the factor by which the population increases per unit of time. It is given the symbol λ (lambda). The value of λ us approximately equal to the average number of offspring produced per parent.

For example, if each pair of parents produces 2 offspring, the number produced per parent would be 2/2m, or 1, giving the λ a value of 1. If each pair of parents produces 3 offspring, the number produced per parent would be 3/2 for a λ value of 1.5.

Substitute λ for er in the equation above to use the following simpler equation:

N(t) = N(0) λt

As an example of the calculation using this equation, consider a population that initially includes 100 individuals, 50 male and 50 female. N(0) = 100. What will the population size be when the fifth generation is born (t=5)? In other words, you wish to know N(5), the population size in the fifth generation. You are given the additional information that each pair of parents produces 3 offspring all of which go on to reproduce at the same rate. Therefore, λ has an approximate

value of 3/2 = 1.5. You can now substitute numbers into the equation, as follows, and solve for N(5):

N(5) = 100 x (1.5)5 = 759

Thus, the population size at the time of the fifth generation will be about 759.

Procedure1. Study the table below which gives world human population figures over the past

few hundred years.2. Using the grid provided, plot the information from the table above. The graph

plots population vs. year. Connect the points smoothly using a solid curve line.3. Calculate λ given the population sizes in 1975 and 2000.4. Using 6 billion as the value of N(0) in the year 2000, estimate the size of the

human population in the years 2025, 2050, 2075, and 2100. Assume that each generation is 25 years long. Also assume that λ has the same value as that calculated in question 3; in other words, growth will continue at the same rate as in the recent past. Add these data points to your graph. Connect the points smoothly to the original curve using a dotted line.

5. Repeat the calculations you made in question 4 but this time assume that each pair of parents produces only 2 offspring (λ is approximately equal to 2/2 or 1). Add these data points to your graph. Connect them smoothly o the original curve using a dashed line.

Date (CE) Population Size1550 500,000,0001700 700,000,0001850 1,000,000,0001900 1,400,000,0001925 1,800,000,0001950 2,500,000,0001975 4,000,000,0002000 6,000,000,0002025 9,000,000,000 6,000,000,0002050 13,500,000,000 6,000,000,0002075 20,250,000,000 6,000,000,0002100 30,375,000,000 6,000,000,000

Analysis and Conclusions1. When I prepared this activity I wanted you to add the Earth’s carrying

capacity to the graph. However, I was unable to find a number for the carrying capacity. Suggest at least five reasons why this might be:

2. What sustainability problems are created by rapid population growth?

3. What do you think would ultimately happen if the human population continued to grow at the current rate?

4. What are some reasons why the Earth can support such a huge human population?

5. What are some solutions to population growth around the world?

6. Which do you think has a greater impact on the Earth – the United States’ 307 million population covering 3,537,441 square miles or India’s 1.139 billion population covering 1,269,219 square miles? Explain.