# Math Behind the Market - Finance in the Classroom

advertisement ```Applications that Apply to Me!
Exponential Function
 What do we know about exponents?
 What do we know about functions?
Exponential Functions
 Always involves the equation: bx
 Example:

23 = 2 &middot; 2 &middot; 2 = 8
Group investigation:
x
Y = 2
 Create an x,y table.
 Use x values of -1, 0, 1, 2, 3,
 Graph the table
 What do you observe.
The Table: Results
X
-1
0
1
2
3
F(x) = 2x
2-1 = &frac12;
20 = 1
21 = 2
22 = 4
23 = 8
The Graph of y =
x
2
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 5 years?
 Show work.
Money Doubling
Year 1: \$100 &middot; 2 = \$200
Year 2: \$200 &middot; 2 = \$400
Year 3: \$400 &middot; 2 = \$800
Year 4: \$800 &middot; 2 = \$1600
Year 5: \$1600 &middot; 2 = \$3200
Earning Interest on
 You have \$100.00.
 Each year you earn 10% interest.
 How much \$ do you have in 5 years?
 Show Work.
Earning 10% results
Year 1: \$100 + 100&middot;(.10) = \$110
Year 2: \$110 + 110&middot;(.10) = \$121
Year 3: \$121 + 121&middot;(.10) = \$133.10
Year 4: \$133.10 + 133.10&middot;(.10) = \$146.41
Year 5: \$146.41 + 1461.41&middot;(.10) = \$161.05
Growth Models: Investing
The Equation is:
A = P (1+
t
r)
P = Principal
r = Annual Rate
t = Number of years
Using the Equation
 \$100.00
 10% interest
 5 years
 100(1+ 100&middot;(.10))5 = \$161.05
 What could we figure out now?
Comparing Investments
 Choice 1
 \$10,000
 5.5% interest
 9 years
 Choice 2
 \$8,000
 6.5% interest
 10 years
Choice 1
\$10,000, 5.5% interest for 9 years.
Equation:
\$10,000 (1 + .055)9
Balance after 9 years: \$16,190.94
Choice 2
\$8,000 in an account that pays 6.5%
interest for 10 years.
Equation:
\$8,000 (1 + .065)10
Balance after 10 years: \$15,071.10
Which Investment?
 The first one yields more money.
 Choice 1: \$16,190.94
 Choice 2: \$15,071.10
Exponential Decay
Instead of increasing, it is decreasing.
Formula: y = a (1 – r)t
a = initial amount
r = percent decrease
t = Number of years
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
Depreciation
Rate
10%
Value after
2 years
\$16,200
Value after
5 years
\$11,809.80
Value after
8 years
\$8609.34
Formula: y = a (1 – r)t
a = initial amount
r = percent decrease
t = Number of years
Value after
10 years
\$6973.57
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.
Assignment
 2 Worksheets:
 Exponential Growth: Investing Worksheet
(available at ttp://www.uen.org/Lessonplan/preview.cgi?LPid=24626)
 Exponential Decay: Car Depreciation
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