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Warm Up Activity: Put yourselves into groups of 2-4 Complete the Dice Activity together

Warm Up Activity: Put yourselves into groups of 2-4 Complete the Dice Activity together Materials needed: Worksheet 36 Die. Exponential Functions. Let’s compare Linear Functions and Exponential Functions. Suppose you have a choice of two different jobs when you graduate college:

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Warm Up Activity: Put yourselves into groups of 2-4 Complete the Dice Activity together

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  1. Warm Up Activity: • Put yourselves into groups of 2-4 • Complete the Dice Activity together • Materials needed: • Worksheet • 36 Die

  2. Exponential Functions

  3. Let’s compare Linear Functionsand Exponential Functions

  4. Suppose you have a choice of two different jobs when you graduate college: • Start at $30,000 with a 6% per year increase • Start at $40,000 with $1200 per year raise • Which should you choose?

  5. Which Job? • When is Option A better? • When is Option B better? • Rate of increase changing • Percent of increase is a constant • Ratio of successive years is 1.06 • Rate of increase a constant $1200

  6. Let’s look at another example

  7. Consider a savings account with compounded yearly income What does compounded yearly mean? You have $100 in the account You receive 5% annual interest Complete the table Find an equation to model the situation. How much will you have in your account after 20 years?

  8. Savings Accounts How do they differ? • Simple Interest • I = interest accrued • P = Principle • r = interest rate • t = time • Compound Interest • A = Current Balance • P = Principle • r = interest rate • n = number of times compounded yearly • t = time in years Linear Exponential

  9. Where else in our world do we see exponential models?

  10. Examples of Exponential Models • Money/Investments • Appreciation/Depreciation • Radioactive Decay/Half Life • Bacteria Growth • Population Growth

  11. How can you determine whether an exponential function models growth or decay just by looking at its graph? Graph 1 Graph 2

  12. Exponential growth functions increase from left to right • Exponential decay functions decrease from left to right

  13. How Can We Define Exponential Functions Symbolically? • Notice the variable is in the exponent? • The base is b and a is the coefficient. • This coefficient is also the initial value/y-intercept (when x=0)

  14. Comparing Exponential Growth/Decay in Terms of Their Equations Exponential Growth Exponential Decay for Example: for Example:

  15. Can you automatically conclude that an exponential function models decay if the base of the power is a fraction or decimal? or No– some fractions and decimals have a value greater than one, such as 3.5 and , and these bases produce exponential growth functions

  16. Fry's Bank Account (clip 1)Fry’s Bank Account (clip 2) • On the TV show “Futurama” Fry checks his bank statement • Since he is from the past his bank account has not been touched for 1000 years • Watch the clip above to see how Fry’s saving’s account balance has changed over time • Answer the questions on your worksheet following each clip

  17. One More Example…

  18. Consider a medication: • The patient takes 100 mg • Once it is taken, body filters medication out over period of time • Suppose it removes 15% of what is present in the blood stream every hour Fill in the rest of the table What is the growth factor?

  19. Growth Factor = 0.85 Note: when growth factor < 1, exponential is a decreasing function

  20. Here are Some Videos to Further Explain Exponential Models

  21. The Magnitude of an Earthquake • Exponential Functions: Earthquakes Explained (2:23) • In this clip, students explore earthquakes using exponential models. In particular, students analyze the earthquake that struck the Sichuan Province in China in 2008

  22. The Science of Overpopulation • The Science of Overpopulation (10:18) • This clip shows how human population grows exponentially. There is more of an emphasis on science in this clip then there is about mathematics as a whole.

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