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. 2 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 3

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

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 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 6

Compound Interest Consider an amount A 0 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 A 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 Where e ≈ Note Page 90, 91 9

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

Assignment Lesson 2.4 Page 106 Exercises 3 – 47 EOO 11