Here are some resources to help you understand the exponential functions that we are studying:
- The Khan Academy has an entire sequence of videos on exponential and logarithmic functions. Here is the first video in the sequence, introducing the exponential functions:
Subsequent videos discuss graphing exponential functions and applications (i.e., word problems) involving exponential growth.
- Here are slides for a lecture on exponential growth and decay, using the world’s population, radioactive waste, carbon dating, and compound interest as examples.
- The exponential model of population growth is often called the Malthusian growth model, “named after the Reverend Thomas Malthus, who authored An Essay on the Principle of Population (1798), one of the earliest and most influential books on population.”
- A related mathematical model of population growth is the logistic model. It is described in Example 10 in Section 5.2 of the textbook (“Inhibited Population Growth”). You can read more about that model in the “Logistic function” Wikipedia entry.