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 2 WORKED EXAMPLE-WRITING EXPONENTIAL GROWTH MODELS/DOUBLING TIME A city has a current population of 5500 people with a growth rate of 12% per year. Write the exponential model for this population and determine the time (to the nearest year) for the population to double. First, determine the EXPONENTIAL MODEL using the information given in the problem. Given: Initial population = 5500 Given: Growth rate of 12% per year Formula to use: P(t) = ab t a = 5500 (initial population) To find b, convert 12% to a decimal (.12), Then, since the population grows, b = 1 + .12 = 1.12 (This value is also called the GROWTH FACTOR). Write the model: P(t) = 5500(1.12) t Second, determine the time for the population to double (DOUBLING TIME) Given: P(t) = 5500(1.12) t , initial population = 5500 Goal: Determine the time for the population to double. Another way to say this is, “find the value of t when the population is twice the initial population” (i.e. find t when P(t) = 2(5500) = 11000). Mathematically, we want to solve the equation: 5500(1.12) t =11000 Use calculator entering Y1 = 5500(1.12) t and Y2 = 11000. Use window X[0..10], Y[0..12000] then 2 nd >Calc>5:Intersect to get t = 6.12. (See graph below). Round to get t = 6. Result: The population will double in about 6 years. Steps to Write an Exponential Growth Model Given the Rate of Growth 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 ADD it to 1. This is your value for “b” (GROWTH 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 Doubling Time Start with an exponential growth model, i.e. P(t) = ab t Set up the equation ab t = 2a Solve by graphing and INTERSECTION method Scottsdale Community College Page 124 Intermediate Algebra
Lesson 3b – More Exponential Functions Mini-Lesson Problem 3 YOU TRY- WRITING EXPONENTIAL GROWTH MODELS/DOUBLING TIME After graduating from college in 2010, Sara accepts a job that pays $52,000 per year. At the end of each year, she expects to receive a 3% raise. a) Let t represent the number of years Sara works at her new job. Write the exponential growth function, S(t), that models her annual salary given the information above. Initial Salary (a value): __________ Given growth rate as a decimal: ___________ Growth factor (b value): _______________ Write the model: S(t) = InitialValue(GrowthFactor) t = ____________________ b) If Sara’s salary continues to increase at the rate of 3% each year, determine how much will she will make in 2015. Show your work clearly here. c) How many years will she have to work before her salary will be double what it was in 2010 (assuming the same growth rate)? Be sure to set up and clearly identify the DOUBLING equation. Then, draw a sketch of the graph you obtain when using the INTERSECTION method to solve. Round to the nearest WHOLE year. DOUBLING EQUATION: ____________________________________ DOUBLING TIME (Rounded to nearest whole year): _________________________ Scottsdale Community College Page 125 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 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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