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Exponential Functions

Exponential Functions. Lesson 2.4. Aeronautical Controls. Exponential Rate Offers servo travel that is not directly proportional to stick travel.

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Exponential Functions

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  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 ≈ 2.71828 • 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

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