Intermediate Algebra – Student Workbook – Second Edition 2013

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

Lesson 3b – More Exponential Functions Mini-Lesson Problem 8 WORKED EXAMPLE–WRITING EXPONENTIAL MDLS USING EXP REGRESSION As with LINEAR FUNCTIONS, we can work with a data table and, if appropriate, model that data using EXPONENTIAL REGRESSION. The steps are almost the same as those followed for LINEAR REGRESSION. The table below shows the population decay in a given state after t years. t (years) Population 5 5,234,456 10 4,892,345 15 4,012,345 Use the Exponential Regression feature of your calculator to generate a mathematical model for this situation. Round “a” to the nearest whole number and “b” to 3 decimals. Press STAT>EDIT>ENTER to show data entry area. The STAT button is on the second row, third column. Data entry area should be blank to begin. To clear, go column by column. Scroll to column header using the arrow keys then press Clear>Enter. Use the arrow keys to move back and forth. [Note: If you ever accidentally DELETE a column, then go to STAT>5: SetUpEditor>ENTER. When you go back to STAT, your column should be restored.] Enter input data into L 1 : 5 ENTER 10 ENTER 15 ENTER Arrow over to the first entry spot in L 2 Enter output data into L 2 : 5234456 ENTER 4892345 ENTER 4012345 ENTER [Note: The numbers for L2 are displayed using scientific notation (the E notation) since they are too long for the column width. Scroll to each number and see its full representation in the bottom of the window. See example highlighted at right. Press STAT>CALC>0:ExpReg>ENTER>ENTER to get the screen at right. Thus, your exponential function (with values rounded as the problem indicates) is y = 6110390(0.974) x . Convert this to the problem’s notation to get P(t) = 6110390(0.974) t . Scottsdale Community College Page 130 Intermediate Algebra
Lesson 3b – More Exponential Functions Mini-Lesson Problem 9 YOU TRY – WRITING EXPONENTIAL MODELS USING EXP REGRESSION Determine the exponential regression equation that models the data below: X 0 1 2 4 6 9 12 16 y 125 75 50 32 22 16 10 5.7 When you write your final equation, round “a” to 1 decimal place and “b” to three decimal places. a) Write final exponential regression equation here: ____________________________ [Note: You may think it strange that your equation does NOT use 125 as the “a” value. That is because of the regression process used by your calculator.] b) What is the rate of decay (as a %) for this equation? _________________________ c) Using your equation from part a, determine y when x = 20 and show your work here. Write the corresponding ordered pair result. [Hint: This is a “Given Input, Find Output” problem] d) Using your equation from part a, determine x when y = 28 and show your work here. Write the corresponding ordered pair result. [Hint: This is a “Given Output, Find Input” problem] e) Using your equation from part a), set up and solve the halving equation. What solution method did you use? HAVLING EQUATION: ________________ HALVING TIME: ______________ Scottsdale Community College Page 131 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 2b - Functions and Function
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Lesson 6a - Exponents and Rational
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Lesson 6b - Rational Exponents & Ra
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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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