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 This next example is long but will illustrate the key difference between EXPONENTIAL FUNCTIONS and LINEAR FUNCTIONS. Problem 2 WORKED EXAMPLE – DOLLARS & SENSE On December 31st around 10 pm, you are sitting quietly in your house watching Dick Clark's New Year's Eve special when there is a knock at the door. Wondering who could possibly be visiting at this hour you head to the front door to find out who it is. Seeing a man dressed in a three-piece suit and tie and holding a briefcase, you cautiously open the door. The man introduces himself as a lawyer representing the estate of your recently deceased great uncle. Turns out your uncle left you some money in his will, but you have to make a decision. The man in the suit explains that you have three options for how to receive your allotment. Option A: $1000 would be deposited on Dec 31st in a bank account bearing your name and each day an additional $1000 would be deposited (until January 31st). Option B: One penny would be deposited on Dec 31st in a bank account bearing your name. Each day, the amount would be doubled (until January 31st). Option C: Take $30,000 on the spot and be done with it. Given that you had been to a party earlier that night and your head was a little fuzzy, you wanted some time to think about it. The man agreed to give you until 11:50 pm. Which option would give you the most money after the 31 days??? A table of values for option A and B are provided on the following page. Before you look at the values, though, which option would you select according to your intuition? Without “doing the math” first, I would instinctively choose the following option (circle your choice): Option Option Option A B C Scottsdale Community College Page 98 Intermediate Algebra
Lesson 3a – Introduction to Exponential Functions Mini-Lesson Option A: $1000 to start + $1000 per day Option B: $.01 to start then double each day Note that t = 0 on Dec. 31st Table of input/output values Table of input/output values t = time in # of days A(t)= $ in account after t days t = time in # of days B(t) = $ in account after t days 0 1000 1 2000 2 3000 3 4000 4 5000 5 6000 6 7000 7 8000 8 9000 9 10,000 10 11,000 11 12,000 12 13,000 13 14,000 14 15,000 15 16,000 16 17,000 17 18,000 18 19,000 19 20,000 20 21,000 21 22,000 22 23,000 23 24,000 24 25,000 25 26,000 26 27,000 27 28,000 28 29,000 29 30,000 30 31,000 31 32,000 0 .01 1 .02 2 .04 3 .08 4 .16 5 .32 6 .64 7 1.28 8 2.56 9 5.12 10 10.24 11 20.48 12 40.96 13 81.92 14 163.84 15 327.68 16 655.36 17 1,310.72 18 2,621.44 19 5,242.88 20 10,485.76 21 20,971.52 22 41,943.04 23 83,886.08 24 167,772.16 25 335,544.32 26 671,088.64 27 1,342,177.28 28 2,684,354.56 29 5,368,709.12 30 10,737,418.24 31 21,474,836.48 WOWWWWW!!!!!!! What IS that number for Option B? I hope you made that choice… it’s 21 million, 4 hundred 74 thousand, 8 hundred 36 dollars and 48 cents. Let’s see if we can understand what is going on with these different options. Scottsdale Community College Page 99 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 4b - More on Logarithms Mini
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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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