Chapter 15
Deeper Exploration of Logs and Exponentials¹

Not all of the models that we can use to describe real world data are based on power functions or polynomials. In fact, we saw in earlier chapters that there are many situations where exponential or logarithmic models may be needed. We also developed a way of interpreting the coefficients of these models using parameter analysis. However, parameter analysis does not give us the power needed to locate maxima and minima for such models. Only calculus tools, specifically the derivative, can do this. In this chapter, you will work with the derivatives of exponential and logarithmic functions, and you will further apply these tools to analyze models of the business world. When you have finished this chapter, you will know how to deal with many of the basic functions found in the real world. The symbolic analysis portion of this chapter will show you how, using multiplication, division and composition of models, we can build many more types of models and analyze them using calculus.