Exponential Functions Lesson 2.4
Exponential Functions
Lesson 2.4
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.
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What airplane is this?
What airplane is this?
General Formula
All exponential functions have the general format:
Where• A = initial value• B = growth rate• t = number of time periods
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( ) tf t A B
Typical Exponential Graphs
When B > 1
When B < 1
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( ) tf t A B
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
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x ya a
9 27x
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
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I P r t
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
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0 1m t
n
rA A
m
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?
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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 ≈ 2.71828
Note Page 90, 919
lim 1m t
r t
m
rP P e
m
Continuous Compounding
Try our $1000 at 3.5% for 6 years using
Compare to with large m
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r tP e
0 1m t
n
rA A
m
Assignment
Lesson 2.4
Page 106
Exercises 3 – 47 EOO
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