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Unit
4 Exponential and Logarithmic Functions This chapter focuses on the definition of a function and how to graph a function and the relationship of functions and their graphs.
Section 4.4 Solving exponential and
logarithmic equations Method I Algebraic example: 2x + 4 = 17 2x = 13 isolate the exponential function ln(2x ) = ln( 13) take logarithm of both sides. x ln 2 = ln 13 use power property x = ln13/ln 2 = 3.700 solve for x
Method II Method III
Similar methods can be used for logarithmic equations. However, in order to graph logarithms with bases other than 10 or e you must use the change of base formula in section 3. Log 4 (x )would be converted to log(x) / log4
Section 4.5 Exponential and Logarithmic Models This section explores real world applications to exponential and logarithmic equations. It is here for informational purposes to show you how the mathematics that you are learning is pertinent to solving real world problems. In the next section we will see how some of these models are created with the use of regression analysis.
Section 4.6 Exploring Data This section explores the method used to fit real life date to mathematical models for the use of analysis and forecasting. In previous chapters linear regression was studied. This section goes further in developing models that may be quadratic, logarithmic, or exponential in nature. the calculator has built in function for many of these regression models . Highlights and Objectives You will be able to:
After entering the data choose the model for best fit from the list on the calculator. STAT CALC PAGE 377 #28
Try other models ( such as QUADREG, or
QUART REG on the same data to see which fits best. The r number,
here equal to .9650891866 tells the goodness of fit. The closer
this number is to 1 the better regression curve fits the data
points.
Review Exercises and Chapter Test At the end of this chapter and every chapter are the review exercises and the chapter test. These are done for you on the CD and also in the solutions manual. As with all the exercises in this course, try to do them on your own first before looking at the given answers and solutions. Remember to post question on the bulletin board and also to E-mail the instructor if you are having difficulty. Do not start the next chapter until you have mastered the material in this chapter. ©Joan Bookbinder 1998 2002 All rights reserved
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