Download presentation

Presentation is loading. Please wait.

1
Warm up Graph

2
**Objective: To use the exponential function y = ex**

Lesson 11-3 The Number e Objective: To use the exponential function y = ex

3
**Natural Base e Like and ‘i’, ‘e’ denotes a number.**

Called The Euler Number after Leonhard Euler ( ) It can be defined by: e= … 0! 1! 2! 3! 4! 5! = ½ + 1/6 + 1/24 + 1/ ≈ ….

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 ….. Which is the value of e.

5
**Using a calculator Evaluate e2 using a graphing calculator**

7.389 Evaluate e2 using a graphing calculator Locate the ex button you need to use the second button

6
**Graphing examples Graph y=ex**

Remember the rules for graphing exponential functions! The graph goes thru (0,1) and (1,e) (1,2.7) (0,1)

7
Graphing cont. Graph y=e-x (1,.368) (0,1)

8
**A = Pert Using e in real life.**

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 = Pert

9
**Example of continuously compounded interest**

You deposit $ 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=Pert = 1000e.08*1 ≈ $

10
Practice An amount of $1, is deposited in a bank paying an annual interest rate of 2.85 %, compounded continuously. Find the balance after 2½ years. A = 1240e(.0285)(2.5) = $1,331.57 A = 1240e(.0285)(2.5) = $1,331.57

11
Exponential Decay An artifact originally had 12 grams of carbon-14 present. The decay model A = 12e t describes the amount of carbon-14 present after t years. How many grams of carbon-14 will be present in this artifact after 10,000 years? A = 12e t A = 12e (10,000) A = 12e-1.21 A = 3.58

12
Sources myteacherpages.com/webpages/rrowe, 2/22/14.

Similar presentations

Presentation is loading. Please wait....

OK

Exponential Functions and Their Graphs Digital Lesson.

Exponential Functions and Their Graphs Digital Lesson.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on world environment day 2011 Ppt on amplitude shift keying demodulation Ppt on depth first search graph Download ppt on global warming Ppt on infosys narayana murthy Ppt on sources of energy for class 8th examination Types of window display ppt on tv Ppt on 360 degree performance appraisal Ppt on money and credit download Ppt on pathophysiology of obesity