1. Applications Growth and Decay Math of Finance
Lesson 2.6

2. Consider Radioactive Half Life

3. 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)

4. 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

5. 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

6. 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

7. 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"
For continuous compounding

8. Present Value Try it out … Find the present value of $45,678.93 if …
Interest is 12.6%
Compounded monthly for 11 months

9. Assignment
Lesson 2.6A
Page 133
Exercises 7 – 39 odd

10. Assignment Lesson 2.6B Page 133
Exercises 16, 18, 20, 22, , 43, 45, 47