Intermediate Algebra – Student Workbook – Second Edition 2013

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$Lesson 2a – Assessment - Scottsdale Community College - Math Blog$

Lesson 3a – Introduction to Exponential Functions Mini-Lesson Writing Exponential Equations/Functions Given a set of data that can be modeled using an exponential equation, use the steps below to determine the particulars of the equation: 1. Identify the initial value. This is the a part of the exponential equation y = ab x . To find a, look for the starting value of the data set (the output that goes with input 0). 2. Identify the common ratio, b, value. To do this, make a fraction of two consecutive outputs (as long as the inputs are separated by exactly 1). We write this as the fraction y 2 y 1 to indicate that we put the second y on top and the first on the bottom. Simplify this fraction and round as the problem indicates to obtain the value of b. 3. Plug in the values of a and b into y = ab x to write the exponential equation. 4. Replace y with appropriate notation as needed to identify a requested exponential FUNCTION. Problem 14 MEDIA EXAMPLE – WRITING EXPONENTIAL EQUATIONS/FUNCTIONS The growth of the population of a small city is shown in the following table: Year Population 2000 12,545 2001 15269 2002 18584 Assume this growth is exponential. Let t = 0 represent the year 2000 and let a equal the initial population in 2000. Let b equal the ratio in population between the years 2001 and 2000. a) Write the equation of the exponential mathematical model for this situation. Round any decimals to two places. Be sure your final result uses proper function notation. b) Using this model, forecast the population in 2008 (to the nearest person). c) Also using this model, determine the nearest whole year in which the population will reach 50,000. Scottsdale Community College Page 110 Intermediate Algebra
Lesson 3a – Introduction to Exponential Functions Mini-Lesson GUIDELINES FOR SELECTING WINDOW VALUES FOR INTERSECTIONS While the steps for using the INTERSECTION method are straightforward, choosing values for your window are not always easy. Here are some guidelines for choosing the edges of your window: First and foremost, the intersection of the equations MUST appear clearly in the window you select. Try to avoid intersections that appear just on the window’s edges, as these are hard to see and your calculator will often not process them correctly. Second, you want to be sure that other important parts of the graphs appear (i.e. where the graph or graphs cross the y-axis or the x-axis). When choosing values for x, start with the standard XMin = -10 and Xmax = 10 UNLESS the problem is a real-world problem. In that case, start with Xmin=0 as negative values for a world problem are usually not important. If the values for Xmax need to be increased, choose 25, then 50, then 100 until the intersection of graphs is visible. When choosing values for y, start with Ymin = 0 negative values of Y are needed for some reason. For Ymax, all equations I am working with need to appear. So, if solving something like 234(1.23) x = 1000, then choose Ymax to be bigger than 1000 (say, 1500). If the intersection does not appear in the window, then try to change only one window setting at a time so you can clearly identify the effect of that change (i.e. make Xmax bigger OR change Ymax but not both at once). Try to think about the functions you are working with and what they look like and use a systematic approach to making changes. Problem 15 YOU TRY – WINDOW VALUES AND INTERSECTIONS In each situation below, you will need to graph to find the solution to the equation using the INTERSECTION method described in this lesson. Fill in the missing information for each situation. a) Solve 54(1.05) x =250 Y1=________ WINDOW Xmin=____, Xmax= ______ Y2 = _______ Ymin=____, Ymax= ______ Solution: x = ______________ Round to two decimals. b) Solve 2340(0.82) x = 1250 Y1=________ WINDOW Xmin=____, Xmax= ______ Y2 = _______ Ymin=____, Ymax= ______ Solution: x = ______________ Round to two decimals. c) Solve 45=250(1.045) x Y1=________ WINDOW Xmin=____, Xmax= ______ Y2 = _______ Ymin=____, Ymax= ______ Solution: x = ______________ Round to two decimals. Scottsdale Community College Page 111 Intermediate Algebra
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Scottsdale Community College Interm
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Table of Contents Lesson 1a - Intro
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Lesson 1a - Introduction to Functio
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Lesson 1b - Linear Equations In the
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Lesson 1b - Linear Equations Mini-L
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Lesson 4b - More on Logarithms This
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Lesson 5a - Introduction to Quadrat
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Lesson 6a - Exponents and Rational
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Lesson 6b - Rational Exponents & Ra
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Lesson 6b - Rational Exponents and
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Appendix A: You Try Answers Lesson
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Appendix A: You Try Answers You Try
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Intermediate Algebra – Student Workbook – Second Edition 2013

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