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Understanding Exponential Growth and Decay: Real-Life Examples and Applications

Explore the concepts of exponential growth and decay through relatable real-life examples. This guide covers fascinating scenarios, such as population dynamics, the depreciation of car and house values, and the rising costs of college tuition. Learn to identify and apply exponential growth and decay formulas effectively, including how to calculate real-world financial decisions. Engage with various practical mathematical exercises, enhancing your understanding of growth patterns that change at accelerated rates.

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Understanding Exponential Growth and Decay: Real-Life Examples and Applications

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  1. Simplify • 3 x 104 ∙ 5 x 105 • 15 x 109 b) 1.5 x 1010 • c) 15 x 1020

  2. Real life examples of Exponential Growth

  3. Projected World Population 6,896,822,16918:22 UTC (EST+5) Jan 30, 2011 Actual

  4. 8.5 and 8.6: Exponential Growth and Decayy = abx Linear Exponential Growth Exponential Decay

  5. Y = 2∙ 3x

  6. Exponential Growth, Exponential Decay, or Neither (linear)?

  7. Exponential Growth Exponential Decay y = a ( 1 + r ) t y = a ( 1 - r ) t a = t = r = (always change r to a ____________)

  8. Mr. Luttrell’s first car purchased was a used 2000 Chevy Cavalier. Brand new, the car cost $14,500. The car depreciates in value by 15% per year. How much did Mr. Luttrell pay for his car in 2004? $14,500 y = a ( 1 - r ) t a= r= t=

  9. Identify which situation represents exponential growth: Jim earns $5 for each A on his report card. The population of California increases at a rate of 5.6% per year. A house’s value depreciates at a rate of 3% per year.

  10. Identify which situation represents exponential decay: Jim’s pay doubles every year. Barbara tips 18% at a restaurant. Annie’s boat’s value depreciates at a rate of 20% per year.

  11. Which table represents exponential growth? a) b) c)

  12. Which table represents exponential decay? a) b) c)

  13. The value of Ed’s house depreciates (loses value) at a rate of .5% per year. If he bought the house for $180,000 , what is the value of his house after 30 years? a.) y = 180,000( 1 + .5)30 b.) y = 180,000( 1 - .005)30 c.) y = 180,000( 1 - .5)30

  14. College isn’t cheap…. At Otterbein University, the current tuition is $36,300 for tuition and room and board for one year. If the costs of tuition increases every year by 3%, what will be the cost when you start college in 5 years? ….. Start saving now! a.) y = 36,300(1+.03)5 a)$41,734!!!! b.) y = 36,300(1 - .03)5 c.) y = 36,300(1 + 3)5

  15. Evaluate when x = -2 and y = -3 x2 y3 x

  16. Y = 2000 (1 + .055)5 b.) y = 18,000(1 + .055)5 c.) y = 2000(1 + 5.5)5 d.) y = 18,000(1 + 5.5)5

  17. Exponential Growth Exponential Decay Linear

  18. Y = 200 (.5)x Exponential Growth Exponential Decay Linear

  19. Y = 3x Exponential Growth Exponential Decay Linear

  20. Y = 2x + 8 Exponential Growth Exponential Decay Linear

  21. Which table represents exponential growth? a) b) c)

  22. George put $500 in the bank at 3% interest for 8 years. How much money did he have at the end of the 8 years if he made no deposits or withdraws? a) $32768000 $633.39 $391.87

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