Applied Calculus 5th Edition

C SPREADSHEET PROJECTS

The following projects require the use of a spreadsheet. They can all be done using only the ideas in Chapter 1. In addition, Project 9 (Verhulst: The Logistic Model) and Project 10 (The Spread of Information) give another perspective on material in Chapters 4 and 9. Project 4 (Comparing Home Mortgages) uses a geometric series but can be done before Chapter 10.

1. MALTHUS: POPULATION OUTSTRIPS FOOD SUPPLY

In this project, we compare exponential and linear growth. We see the eventual dominance of exponential functions over linear functions.

One of the most famous models of population growth was made by Thomas Malthus in the early 19^th century. Malthus believed that while human population increased exponentially, its means of subsistence increased linearly. The gloomy conclusion that Malthus drew from this observation was that the population of the earth would inevitably outstrip its means of subsistence, resulting in an inadequate supply of food. (Malthus went on to note that this state of affairs could only be averted by war, famine, epidemic disease, wide-scale sexual restraint, or other such drastic checks on population growth.)

The following table shows part of a spreadsheet showing such as a scenario.¹⁶ The starting population is 1 million, while the available food feeds 2 million people. The population grows at an annual rate of 3% per year and the food production increases by 100,000 per year. These population and food growth rates are in cells on the ...