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Mastering Mathematical Properties & Equations

Learn to classify numbers, solve multi-step equations, graph exponential growth, and apply proportions and inequalities. Explore real-world examples of exponential decay, compound interest, and geometric sequences. Perfect your skills in exponential modeling and decay scenarios. Master graphing standard and slope-intercept forms effectively.

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Mastering Mathematical Properties & Equations

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  1. Let’s Review • Mathematical Properties • Classify Numbers • Multi-Step Equations • Absolute Value • Proportions/Percent of increase/decrease • Inequalities : When to switch sign? • Graphing Standard Form • Slope-Intercept Form • Geometric Sequences • Graph Exponential Equations by hand or Calculator • B.A.G.

  2. Unit 6 Lesson 3

  3. “I can…” • …write exponential equations to model growth & decay scenarios, including percent change • M(F&A)-10-2

  4. Exponential Growth

  5. Example 1: Exponential Growth • Since 2005 the amount of $ spent at restaurants in the US has increased by 7% each year. • In 2005, about $360 billion was spent at restaurants. • How much will be spent in the year 2015 if this trend continues? • Don’t forget the units!

  6. Special application of Exponential growth

  7. Example 2: Compound Interest • Determine the amount of an investment if $1000 is invested at an interest rate of 7.25% compounded quarterly for 7 years

  8. Try # 5 in your homework packet • Page 611 • 4 minutes…

  9. Chernobyl-Uninhabited • 1986; nuclear reactor accident • Toxic, radioactive chemicals; plutonium • Initial amount of 10 pounds • Half-life of 24,100 years • How much remains in 2015? After 100,000 years?

  10. Exponential Decay

  11. Example 3 • A farmer buys a tractor for $50,000. If the tractor depreciates 10% per year, find the value of the tractor in 7 years

  12. Example 4 • In 1994 the sales of cassette tapes reached its peak of $2,976,400,000. If the annual percent of decrease is 18.6%, predict the sales of cassettes in 2009.

  13. Try # 6, 7 in your homework packet • 4 minutes… • Page 611

  14. Home Work Assignment • Section handout – Page 611, 1-9 ALL

  15. ExitSlip

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