1. 3.5 Exponential Growth & Decay
Applications that Apply to Me!

2. What real-life applications are there?

3. Think-Ink-Pair: Money Doubling?
You have a $100.00
Your money doubles each year.
How much do you have in 5 years?
Show work.

4. 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

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

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

7. a = Principle or starting amount
Growth Models:
The Equation is:
y = a (1+ r)t
a = Principle or starting amount
r = percent increase
t= time

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

9. Comparing Investments
Choice 1 – Bank of America
$10,000
5.5% interest
9 years
Choice 2 – Wells Fargo
$8,000
6.5% interest
10 years

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

11. 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

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

13. 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

14. 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

15. 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
Formula: y = a (1 – r)t
a = initial amount
r = percent decrease
t = Number of years

16. 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.

17. Compound Interest A = Ending Amount P = Starting (principle) Amount
r = interest rate
t= number of years
n = Number of times the
interest is compounded in a year.
*annually = 1 *quarterly = 4
*semi-annually = 2 *monthly = 12

18. Compound Interest Example:
You deposit $5000 into a savings account that earns 3% annual interest. If no other money is deposited, what is your balance after 4 years if it is compounded…
Semi-annually:
Quarterly:
Monthly:
Daily:
Annually: