Are the patterns in the graphs below linear or exponential? The question gets to the heart of the argument that Malthus made. The two graphs show the population change for various countries of the Americas over three time periods. You can look at changes in population during the colonial period from roughly 1650 to 1810, the post colonial period from 1810 to 2000, and more recently from 1960 to 2024. The last time period matches that of the other graph showing changes in a variety of staple food products by decades since the 1960s.
- Select the time Period and Country for the Population Growth graph and the Crop and Country for the Crop Production graph. The crop values are the average annual production in tons over the prior decade.
- Change the function that models the data from Linear to Exponential and you can see which type of pattern best fits the data.
- Hit the Graph button after new selections are made to redraw a graph.
- Equations for each type of function are given along with the correlation coefficient - a value between 0 and 1 in absolute value that indicates the degree to which the mathematical pattern fits the data - 1 being a perfect fit; 0 no fit. A positive value indicates both variables are changing in the same direction; a negative value indicates that as one value increases the other is decreasing.
1) Graph the recent growth (1960 - 2024) of the United States and Canada. Describe how the growth in each country compares with its growth during the colonial period?
2) When you graph the population growth exponentially for each country the equation of the curve that best fits the data is given in the form y = a(ebx), where b represents the rate of growth. When you graph Ireland's exponential growth rate from 1650 to 1810, for example, the equation is y = 1.86(e0.007x) . The population's growth rate during this period was, thus, 0.7% per year How does this compare with the growth rates in England's American colonies and the Spanish colonies in Mexico and Peru?
3) Select two countries in the Americas and look at the change in production of their staple foods. Was the change linear or exponential? Discuss.
Population data from Jonathan Fink-Jensen, Total
Population, (IISH Dataverse, 2015), downloaded
October 15, 2017.
Staple food data from FAOSTAT: Crops, (Food & Agricultural Organization of the United Nations, 2017) downloaded October 15, 2017