Download presentation

Presentation is loading. Please wait.

Published bySophia Bradshaw Modified over 3 years ago

1
8.3 The number e p. 480

2
The Natural base e Much of the history of mathematics is marked by the discovery of special types of numbers like counting numbers, zero, negative numbers, Л, and imaginary numbers.

3
Natural Base e Like Л and i, e denotes a number. Called The Euler Number after Leonhard Euler (1707-1783) It can be defined by: e= 1 + 1 + 1 + 1 + 1 + 1 +… 0! 1! 2! 3! 4! 5! = 1 + 1 + ½ + 1/6 + 1/24 + 1/120+... 2.718281828459….

4
The number e is irrational – its decimal representation does not terminate or follow a repeating pattern. The previous sequence of e can also be represented: As n gets larger (n), (1+1/n) n gets closer and closer to 2.71828….. Which is the value of e.

5
Examples e 3 · e 4 = e 7 10e 3 = 5e 2 2e 3-2 = 2e (3e -4x ) 2 9e (-4x)2 9e -8x 9 e 8x

6
More Examples! 24e 8 = 8e 5 3e 3 (2e -5x ) -2 = 2 -2 e 10x = e 10x 4

7
Using a calculator Evaluate e 2 using a graphing calculator Locate the e x button you need to use the second button 7.389

8
Evaluate e -.06 with a calculator

9
Graphing f(x) = ae rx is a natural base exponential function If a>0 & r>0 it is a growth function If a>0 & r<0 it is a decay function

10
Graphing examples Graph y=e x Remember the rules for graphing exponential functions! The graph goes thru (0,a) and (1,e) (0,1) (1,2.7) y=0

11
Graphing cont. Graph y=e -x (0,1) (1,.368) y=0

12
Graphing Example Graph y=2e 0.75x State the Domain & Range Because a=2 is positive and r=0.75, the function is exponential growth. Plot (0,2)&(1,4.23) and draw the curve. (0,2) (1,4.23) y=0

13
Using e in real life. In 8.1 we learned the formula for compounding interest n times a year. In that equation, as n approaches infinity, the compound interest formula approaches the formula for continuously compounded interest: A = Pe rt

14
Example of continuously compounded interest You deposit $1000.00 into an account that pays 8% annual interest compounded continuously. What is the balance after 1 year? P = 1000, r =.08, and t = 1 A=Pe rt = 1000e.08*1 $1083.29

15
Homework P. 483 (17-73) odd

Similar presentations

OK

Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley CHAPTER 5: Exponential and Logarithmic Functions 5.1 Inverse Functions 5.2 Exponential.

Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley CHAPTER 5: Exponential and Logarithmic Functions 5.1 Inverse Functions 5.2 Exponential.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on power steering Ppt on hard gelatin capsule ingredients Ppt on causes of second world war Ppt on cross site scripting internet Ppt on solar power projects Ppt on model view controller Ppt on therapeutic environment in nursing Ppt on quality assurance in engineering education Ppt on unique identification system Moral values for kids ppt on batteries