# Lesson 2.6 - Applications Growth by fjwuxn

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```									   Applications
Growth and Decay
Math of Finance
Lesson 2.6

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Exponential Growth/Decay
If Y0 is the initial quantity present
• The amount present at time t is
k t
y  y0e
This is continuous growth/decay
• Contrast to periodic growth/decay
y  y0bt
Convert between, knowing b = ek
• Result is k ≈ r (recall that b = 1 + r)
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Exponential Growth/Decay
Given growth data, determine continuous
growth function
• Initial population = 2500
• Ten years later, population is 4750
• Assuming continuous growth, what is function
Strategy
• What is y0?
• Use (10,4750), solve for k
• Write function
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Exponential Growth/Decay
For exponential decay
• Recall that 0 < b < 1 and r < 0
• That means k < 0 also
Suppose Superman's nemesis, Kryptonite
has half life of 10 hours?
• How long until it reaches 30% of its full power
and Superman can save the city?
Strategy
• Again, find k using .5 and 10
• Then find t using the .3
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Effective Rate
Given
• r is stated annual rate
• m is number of compounding periods
Then effective rate of interest is

   r
m
rE  er 1
rE  1    1
 m                  For continuous
compounding

Try it … what is effective rate for 7.5%
compounded monthly?                          6
Present Value
Consider the formula for compounded
interest                mt
   r
A  P 1  
 m

Suppose we know A and need to know P
• This is called the "present value"

 t m       P  A  e r t
   r
P  A 1                   For continuous
 m                    compounding
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Present Value
Try it out …

Find the present value of \$45,678.93 if …
• Interest is 12.6%
• Compounded monthly for 11 months

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Assignment

Lesson 2.6A
Page 133
Exercises 7 – 39 odd

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Assignment

Lesson 2.6B
Page 133
Exercises 16, 18, 20, 22,
41, 43, 45, 47

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