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 6 YOU TRY – WRITING EXPONENTIAL DECAY MODELS/HALVING TIME In 1970, the population of Buffalo, New York had a population of 462,768 people. Assume the population decreased by 1.4% each year from 1970 to 2000. a) Let t represent the number of years since 1970 (i.e. your starting year is 1970 so t=0 in this year). Write the exponential decay function, P(t), that models the annual population given the information above. Initial Population (a value): __________ Given DECAY RATE as a decimal: ___________ Take 1 – the DECAY RATE decimal to identify your DECAY FACTOR (b value): _______________ Write the model: P(t) = InitialValue(DecayFactor) t = ____________________ b) If the population continues to decrease at the rate above, determine how many people will live in Buffalo in 2015. Show your work clearly here. c) How many years will it take for the Buffalo population to decrease to half what it was in 1970 (assuming the same decay rate)? Be sure to set up and clearly identify the HALVING equation. Then, draw a sketch of the graph you obtain when using the INTERSECTION method to solve. Round to the nearest WHOLE year. HALVING EQUATION: ___________________________ HALVING TIME (Rounded to nearest whole year): _________________________ Scottsdale Community College Page 128 Intermediate Algebra
Lesson 3b – More Exponential Functions Mini-Lesson Problem 7 YOU TRY – WRITING EXPONENTIAL GROWH/DECAY MODELS Given what we have covered in this lesson so far, you should now be able to quickly write models for exponential growth or decay given a starting value and a rate of growth or decay. Fill in the table below to practice. The first few are done for you. Given Initial population = 12,000 Growth rate = 40% Initial Value (a value) Growth or Decay Factor (b value) 12,000 40% = 0.40 b = 1 + .40 =1.40 Exponential Function y=ab t P(t) = 12,000(1.40) t Initial value = 45 Decay rate = 35% 45 35% = 0.35 b=1 - 0.35=0.65 V(t)=45(0.65) t Initial population = 145 Growth rate 3% Initial value = 314 Decay rate 96.5% Initial population = 412 Growth rate 13.24% Initial investment = 546 Decay rate 2% Initial amount = 3 Decay rate 22% Initial population = 3061 Growth rate 205% Scottsdale Community College Page 129 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 1b - Linear Equations Practi
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Lesson 2a - Linear Functions and Ap
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Lesson 2b - Functions and Function
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Lesson 5a - Introduction to Quadrat
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Lesson 5b - Solving Quadratic Equat
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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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