Do Now

1 / 18

# Do Now - PowerPoint PPT Presentation

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:

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Do Now' - carr

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
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: bx
• Example:
• 23 = 2 · 2 · 2 = 8
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
• 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?
• You have a \$100.00
• Your money doubles each year.
• How much do you have in 3 years?
• Show work.
Money Doubling

Year 1: \$100 · 2 = \$200

Year 2: \$200 · 2 = \$400

Year 3: \$400 · 2 = \$800

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

Year 1: \$100 + 100·(.10) = \$110

Year 2: \$110 + 110·(.10) = \$121

Year 3: \$121 + 121·(.10) = \$133.10

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
• \$100.00
• 10% interest
• 5 years
• 100(1+ (.10))5 = \$161.05
• What could we figure out now?
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
• 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

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

Textbook:

• Page 481 #24-28
• Page 489 #26-30