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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:

ddtAekt=kAekt.

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