Applications Growth and Decay Math of Finance

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# Applications Growth and Decay Math of Finance - PowerPoint PPT Presentation

Applications Growth and Decay Math of Finance. Lesson 2.6. Consider Radioactive Half Life. Exponential Growth/Decay. If Y 0 is the initial quantity present The amount present at time t is This is continuous growth/decay Contrast to periodic growth/decay

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### ApplicationsGrowth and DecayMath of Finance

Lesson 2.6

Exponential Growth/Decay
• If Y0 is the initial quantity present
• The amount present at time t is
• This is continuous growth/decay
• Contrast to periodic growth/decay
• Convert between, knowing b = ek
• Result is k ≈ r (recall that b = 1 + r)
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
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

For continuous compounding

Effective Rate
• Given
• r is stated annual rate
• m is number of compounding periods
• Then effective rate of interest is
• Try it … what is effective rate for 7.5% compounded monthly?

For continuous compounding

Present Value
• Consider the formula for compounded interest
• Suppose we know A and need to know P
• This is called the "present value"
Present Value
• Try it out …
• Find the present value of \$45,678.93 if …
• Interest is 12.6%
• Compounded monthly for 11 months
Assignment
• Lesson 2.6A
• Page 133
• Exercises 7 – 39 odd
Assignment
• Lesson 2.6B
• Page 133
• Exercises 16, 18, 20, 22, 41, 43, 45, 47