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. 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

Typical Exponential Graphs When B > 1 When B < 1

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

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

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

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?

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, 91

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

Assignment Lesson 2.4 Page 106 Exercises 3 – 47 EOO