In this module, you will be introduced to differential equations. The module content is split into four lessons.
- Lesson 4.1: Differential Equations
- Lesson 4.2: Exponential Growth and Decay
- Lesson 4.3: Other Elementary Differential Equations
- Lesson 4.4: Introduction to Direction Fields (also called Slope Fields)
- Do a search on the internet to find fairly reliable estimates for the world’s human population in the years 1960, 1970, 1980, and 1990.
- Assuming that the world’s human population follows an exponential model P(t)=P0ekt, use the 1960 figure as the initial population P0 and the 1970 population figure to find k, the growth rate constant. Note that if t is measured in years and 1960 is the starting year, 1970 corresponds to t=10.
- Compare the populations you found for 1980 and 1990 in part 1 to the values the exponential model you found in part 2 would have predicted.
- Do a search on the internet to find what you consider to be a reliable estimate of the carrying capacity of the earth. Use the model in #2 to estimate when we will reach the carrying capacity.