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 4 MEDIA EXAMPLE – WRITING EXPONENTIAL DECAY MODELS/HALVING TIME The 2000 U.S. Census reported the population of Tulsa, Oklahoma to be 382,872. Since the 2000 Census, Tulsa’s population has been decreasing at approximately 2.6% per year. a) Write an EXPONENTIAL DECAY MODEL, P(t), that predicts the population of Tulsa, OK at any time t. b) Use the function you wrote for P(t) to predict the population of Tulsa, OK in 2013. c) In how many years will the population of Tulsa decrease to 300,000 people (round to the nearest whole year)? d) In how many years will the population of Tulsa decrease to HALF of the initial (2000) population? Round to the nearest whole year. Scottsdale Community College Page 126 Intermediate Algebra
Lesson 3b – More Exponential Functions Mini-Lesson Problem 5 WORKED EXAMPLE – WRITING EXPONENTIAL DECAY MODELS/HALVING TIME In 2012, Shannon purchased a new Ford Mustang GT convertible for $35,300. Since then, the value of the car has decreased at a rate of 11% each year. First, determine the EXPONENTIAL MODEL using the information given in the problem. Given: Purchase price = $35,300 Given: Decay rate of 11% per year Formula to use: V(t) = ab t a = 35,300 (initial value) To find b, convert 11% to a decimal (0.11), Since the population decays, b = 1 – .11 = 0.89 (This value is also called the DECAY FACTOR). Write the model: V(t) = 35300(0.89) t Second, determine the time for the price to halve (HALF-LIFE or HALVING TIME) Given: V(t) = 35300(0.89) t , initial price = $35,300 Goal: Determine the time for the value of the car to halve. Another way to say this is, “find the value of t when the value is half the initial purchase price” (i.e. find t when V(t) = 0.5(35,300) = 17,650). Mathematically, we want to solve the equation: 35300(0.89) t =17650 Use your calculator and enter Y1 = 35300(0.89) t and Y2 = 17650. Use window X[0..10], Y[0..35300] then 2 nd >Calc>5:Intersect to get t = 5.95 (See graph below). Result: The value of the car will be worth half the initial purchase price in about 6 years. Steps to Write an Exponential Decay Model Given the Rate of Decay Determine initial value of the model (i.e. initial population, initial investment, initial salary, etc.). This is the value of the model at time t = 0 and the number will be your number for “a”. Write the given rate as a decimal and SUBTRACT it from 1. This is “b”(DECAY FACTOR). Write the model using appropriate function notation (i.e. P(t) = ab t , V(t) = ab t , S(t) = ab t , etc.) Steps to Determine Halving Time (also called Half-Life) Start with an exponential growth model, i.e. P(t) = ab t Set up the equation ab t = 0.5a Solve by graphing and INTERSECTION method Scottsdale Community College Page 127 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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