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Do Now. Three years ago you bought a Lebron James card for $45. It has appreciated (gone up in value) by 20% each year since then. How much is worth today?. Exponential Growth & Decay. Applications that Apply to Me!. Exponential Functions. Always involves the equation: b x Example:

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do now
Do Now
  • Three years ago you bought a Lebron James card for $45. It has appreciated (gone up in value) by 20% each year since then. How much is worth today?
exponential growth decay

Exponential Growth & Decay

Applications that Apply to Me!

exponential functions
Exponential Functions
  • Always involves the equation: bx
  • Example:
    • 23 = 2 · 2 · 2 = 8
group investigation y 2 x
Group investigation:Y = 2x
  • Create an x,y table.
  • Use x values of -1, 0, 1, 2, 3,
  • Graph the table
  • What do you observe.
observations
Observations
  • What did you notice?
  • What is the pattern?
  • What would happen if x= -2
  • What would happen if x = 5
  • What real-life applications are there?
group money doubling
Group: Money Doubling?
  • You have a $100.00
  • Your money doubles each year.
  • How much do you have in 3 years?
  • Show work.
money doubling
Money Doubling

Year 1: $100 · 2 = $200

Year 2: $200 · 2 = $400

Year 3: $400 · 2 = $800

earning interest on
Earning Interest on
  • You have $100.00.
  • Each year you earn 10% interest.
  • How much $ do you have in 3 years?
  • Show Work.
earning 10 results
Earning 10% results

Year 1: $100 + 100·(.10) = $110

Year 2: $110 + 110·(.10) = $121

Year 3: $121 + 121·(.10) = $133.10

exponential growth model
Exponential Growth Model

The Formula is:

y = a(1+r)t

a = Initial Amount

r = Growth Rate

(1+r) = Growth Factor

t = Time Period

using the equation
Using the Equation
  • $100.00
  • 10% interest
  • 5 years
  • 100(1+ (.10))5 = $161.05
  • What could we figure out now?
exponential decay model
Exponential Decay Model

Instead of increasing, it is decreasing.

Formula: y = a(1–r)t

a = Initial Amount

r = Decay Rate

(1-r) = Decay Factor

t = Time Period

real life examples
Real-life Examples
  • What is car depreciation?
  • Car Value = $20,000
  • Depreciates 10% a year
  • Figure out the following values:
    • After 2 years
    • After 5 years
    • After 8 years
    • After 10 years
exponential decay car depreciation
Exponential Decay: Car Depreciation

Assume the car was purchased for $20,000

Formula: y = a (1 – r)t

a = initial amount

r = percent decrease

t = number of years

homework
Homework

Textbook:

  • Page 481 #24-28
  • Page 489 #26-30