LESSON 3: THE NUMBER e
The Number e? e isn't a number. Is it? Leonard Euler thinks it is. In lessons 1 & 2, we looked at compound growth and decay. The issue is determining the compound interest formula for periodic growth (annually, monthly, etc.). What about quanities that grow/decay all the time? Check out the introduction video below, then grab your Cornell Notes sheet to use as you watch the presentation for lesson 3.
Introduction
SWBAT
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Differentiate between exponential growth and decay functions having a base of e.
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Graph a natural base exponential growth or decay function with a TI-84 calculator or smartphone app.
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Use the continuous interest formula to solve real-life situations involving continuos natural growth.
Absorb
The Number e Presentation
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Use your Cornell Notes to document important information, processes and/or questions you have.
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Notes will be checked and scored for content at the beginning of class on February 24. Make sure to have any questions you have written down for clarification.
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Check out the linked video above for additional information and help.
Do
Practice Problems: 18-60( Divisible by 3),61-66,76,79 (pg.483)
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McDougal Littell - Algebra II - Copyright 2004
Connect
Check out the video above and then open and complete the World Population Growth activity below.
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Download, print and complete the Population Growth activity. You will need an internet connected device to do some research as well as a calculator.
Summary
The number e is also known as Euler's number or the natural base. It is an irrational number (like pi) that is approximately 2.718... It is used in calculating continuous exponential growth and decay of objects in nature (alive). Students should be able to differentiate between exponential growth and decay functions that have a base of e, graph a natural base exponential growth or decay function with a TI-84 calculator or smartphone app. Finally, students should be able to use the continuous interest formula to solve real-life situations involving exponential growth in nature.