Unit4 Exponential and Logarithmic Functions sections 4

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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.

Graphing Calculator Skills needed for this chapter.

Section 4.4 Solving exponential and logarithmic equations
There are many different ways to solve these equations, both algebraically and n the graphing calculator. This section explores many of those ways.

Method I

Algebraic example:

2^x + 4 = 17

2^x = 13 isolate the exponential function

ln(2^x ) = 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

For this method, set
equation equal to zero, then use
2nd CALC 2 to find where the
function equals 0.
For this method ,graph each side
separately and find the point
of intersection using 2nd CALC 5

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

Explore Logarithmic and Exponential equations with LiveMath

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:

Use the regression capabilities of the calculator to fit a curve to given or collected data.

After entering the data choose the model for best fit from the list on the calculator. STAT CALC

PAGE 377 #28

ENTER DATA ( STAT, EDIT) STAT, CALC Choose 9, log regression

Type in L1, L2, Y1 to also have the equation copied to Y1 on the equation editor (Y1 found in VARS menu) ENTER GRAPH, ZOOM 9 graphs the regression equation and the data together.

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.

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Proceed to Unit 5