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

1 / 10

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

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

Applications Growth and Decay Math of Finance

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

## 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