Download Exponential Functions

Exponential Functions
Lesson 2.4
Aeronautical Controls
Exponential Rate
• Offers servo travel that is not directly
proportional to stick travel.
• Control response isWhat
milderairplane
below half-stick, but
becomes increasing is this?
stronger as stick travel
approaches
100%. Great for
aerobatics and
trouble situations.
2
General Formula
All exponential functions have the general
format:
f (t )  A  B
t
Where
• A = initial value
• B = growth rate
• t = number of time periods
3
Typical Exponential Graphs
When B > 1
f (t )  A  Bt
When B < 1
4
Exponential Equations
Given
a a
x
y
• 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
9  27
x
5
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
I  P r t
6
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
r

An  A0 1  
 m
mt
7
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?
8
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
r

lim P 1  
m 
 m
mt
 Pe
r t
• Where e ≈ 2.71828
Note Page 90, 91
9
Continuous Compounding
Try our $1000 at 3.5% for 6 years using
Pe
Compare to
r t
r

An  A0 1  
 m
mt
with large m
10
Assignment
Lesson 2.4
Page 106
Exercises 3 – 47 EOO
11