1. Exponential Functions
Lesson 2.4

2. Aeronautical Controls
Exponential Rate
Offers servo travel that is not directly proportional to stick travel.
Control response is milder below half-stick, but becomes increasing stronger as stick travel approaches 100%. Great for aerobatics and trouble situations.
What airplane is this?

3. General Formula All exponential functions have the general format:
Where
A = initial value
B = growth rate
t = number of time periods

4. Typical Exponential Graphs
When B > 1
When B < 1

5. Exponential Equations
Given
What could you say about x and y?
If the two quantities are equal and the base value for the exponential expression are the same . . .
Then the exponents must be the same
Use to solve exponential equations

6. Simple Interest If you start with an amount P, the principal
and receive interest rate at r%
for time t
Then the interest earned is I, the product of P, r (as a decimal) and t

7. Compound Interest
Consider an amount A0 of money deposited in an account
Pays annual rate of interest r percent
Compounded m times per year
Stays in the account t years
Then the resulting balance At

8. Compound Interest
What happens when we increase the number of compounding periods?
Try $1000 at 3.5% for 6 years
Compounded yearly?
Quarterly
Monthly
Weekly
Daily
For every hour? every minute? every second?

9. The Irrational Number e
As the number of compounding periods increase
The change in the end result becomes less
We reach a limit
Can be shown
Where e ≈
Note Page 90, 91

10. Continuous Compounding
Try our $1000 at 3.5% for 6 years using
Compare to with large m

11. Assignment
Lesson 2.4
Page 106
Exercises 3 – 47 EOO