Chapter 5 A closer look at exponential functions
We have seen how exponential equations help us understand a variety of situations - from investments and loans, to rising health care costs, to population growth, or any quantity increasing at a fixed percentage. But that’s not all. In this chapter we explore other situations in which exponential equations help us understand any type of exponential growth (increasing) as well as exponential decay (decreasing).
We have encountered exponential equations often in this text already, so this chapter begins with a review section on everything we have seen: modeling with exponential equations; interpreting exponential growth, especially the growth factor and percent increase; graphing exponential equations; solving exponential equations using logs; and the connection between percent increase and exponential growth in the first place.
Next, we study exponential growth in more detail, including finding the growth factor when we are not told the percent change. We also study exponential decay, including situations where we know the percentage decrease. After that we compare how linear or exponential equations model situations where it’s not clear which to use. We close with a section on comparing exponential growth to alternative models.
