Chapter 2
Models of Growth: Rates of Change
2.4 Exponential Functions
Section Summary
In this section we have developed formulas for differentiating exponential functions. In particular, we found that
ddtbt=(lnb) bt.
The logarithm in this formula, ln, is the natural logarithm, the one that has Euler's number e as its base. (An approximate value of e is 2.718281828.) When e is also the exponential base, we get the simpler formula
ddtet=et.
This natural exponential function, the one that is its own derivative, is also called exp: that is, expt=et.
More generally, we found a whole family of functions that all have derivatives proportional to themselves:
ddt Aekt=kA ekt.