1. Exponential Growth & Decay
Applications that Apply to Me!

2. Exponential Function What do we know about exponents?
What do we know about functions?

3. Exponential Functions
Always involves the equation: bx
Example:
23 = 2 · 2 · 2 = 8

4. 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.

5. The Table: Results X F(x) = 2x -1 2-1 = ½ 20 = 1 1 21 = 2 2 22 = 4 3
20 = 1 1
21 = 2 2
22 = 4 3
23 = 8

6. The Graph of y = 2x

7. 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?

8. Group: Money Doubling? You have a $100.00
Your money doubles each year.
How much do you have in 5 years?
Show work.

9. Money Doubling
Year 1: $100 · 2 = $200 Year 2: $200 · 2 = $400 Year 3: $400 · 2 = $800 Year 4: $800 · 2 = $1600 Year 5: $1600 · 2 = $3200

10. Earning Interest on You have $100.00. Each year you earn 10% interest.
How much $ do you have in 5 years?
Show Work.

11. Earning 10% results Year 1: $100 + 100·(.10) = $110

12. Growth Models: Investing
The Equation is:
A = P (1+ r)t
P = Principal
r = Annual Rate
t = Number of years

13. Using the Equation $100.00 10% interest 5 years 100(1+.10)5 = $161.05
What could we figure out now?

14. Comparing Investments
Choice 1
$10,000
5.5% interest
9 years
Choice 2
$8,000
6.5% interest
10 years

15. Choice 1 $10,000, 5.5% interest for 9 years.
Equation: $10,000 ( )9
Balance after 9 years: $16,190.94

16. Choice 2 $8,000 in an account that pays 6.5% interest for 10 years.
Equation: $8,000 ( )10
Balance after 10 years: $15,071.10

17. The first one yields more money.
Which Investment?
The first one yields more money.
Choice 1: $16,190.94
Choice 2: $15,071.10

18. Instead of increasing, it is decreasing.
Exponential Decay
Instead of increasing, it is decreasing.
Formula: y = a (1 – r)t
a = initial amount
r = percent decrease
t = Number of years

19. 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

20. Exponential Decay: Car Depreciation
Assume the car was purchased for $20,000
Depreciation
Rate
Value after 2 years
Value after 5 years
Value after 8 years
Value after 10 years
10%
$16,200
$11,809.80 $ $
Formula: y = a (1 – r)t
a = initial amount
r = percent decrease
t = Number of years

21. What Else? What happens when the depreciation rate changes.
What happens to the values after 20 or 30 years out – does it make sense?
What are the pros and cons of buying new or used cars.

22. Assignment 2 Worksheets:
Exponential Growth: Investing Worksheet (available at ttp://
Exponential Decay: Car Depreciation