Are there different kinds of rate of change?

1 Answer
Dec 24, 2014

Yes, there are different kinds of rate of change, since there is more than one way to describe how something is changing and some ways are more useful than others depending on the context. For instance, it might be most valuable to describe an absolute rate of change:

Or alternatively, it might be more useful to describe a rate of change relative to the size of a population or other changing quantity:

Rates of change can also be described differently in terms of time. Some rates are averages, taken over a period of time:

On the other hand, if a changing quantity is defined by a function, we can differentiate and evaluate the derivative at given values to determine an instantaneous rate of change: