Download presentation

1
6.6 The Natural Base, e

2
Natural Base, e The natural base, e, is used to estimate the ages of artifacts and to calculate interest that is compounded continuously.

3
**Natural Exponential Function**

The exponential function with base e, f(x)=ex, is called the natural exponential function. And e is called the natural base. 1 You calculator has a FANCY ex button you can use!!! 2

4
**Evaluate f(x)=ex to the nearest thousandth for each value of x below:**

5
**Exponential Properties**

Are the same for base e!! Simplify the expression. a. e2 e5 = e2 + 5 = e7 b. 12 e4 3 e3 = e4 – 3 4 = 4e (5 ) c. e –3x 2 = 52 ( e –3x ) 2 = 25 e –6x = 25 e6x

6
**Try This! (10 ) Simplify the expression. 1. e7 e4 e11 4. e –4x 3 1000**

2. 2 e–3 6e5 12 e2 Use a calculator to evaluate 3. 24 e8 4 e5 6 e3 2.117

7
**The Graph of the Exponential Function**

1 3 2

8
**Graph natural base functions**

Graph the function. State the domain and range. a. y = 3e 0.25x SOLUTION Because a = 3 is positive and r = 0.25 is positive, the function is an exponential growth function. Plug in 0 and 1. x y 1 The domain is all real numbers, and the range is y > 0.

9
**Graph natural base functions**

Graph the function. State the domain and range. b. y = e –0.75(x – 2) + 1 SOLUTION a = 1 is positive and r = –0.75 is negative, so the function is an exponential decay function. Translate the graph of y = right 2 units and up 1 unit. e –0.75x The domain is all real numbers, and the range is y > 1.

10
**Try This! Graph the function. State the domain and range. y 2e 0.5x =**

domain: all real numbers, range: y>0

11
**Try This! Graph the function. State the domain and range. 1 2 f(x) =**

e -x +1 domain: all real numbers, range: y>1

12
**Continuous Compounding Formula**

If P dollars are invested at an interest rate, r, that is compounding continuously, then the amount, A, of the investment at time t is given by: A = Pert

13
**An investment of $1000 earns an annual interest rate of 7.6%**

Compare the final amounts after 8 years for interest compounded quarterly and for interest compounded continuously. Compounded Quarterly Continuously

14
Find the value: Of $500 after 4 years invested at an annual interest rate of 9% compounded continuously. $716.66

15
Homework Green Book!! Page 142 # 1-25odd #27 and 28

Similar presentations

Presentation is loading. Please wait....

OK

Chapter 4 4-6 The Natural base, e.

Chapter 4 4-6 The Natural base, e.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google

Run ppt on tv Ppt on bluetooth applications download Ppt on natural resources and conservation degrees Ppt on teachers day poems Ppt on obesity prevention cdc Ppt on service oriented architecture interview Ppt on medical tourism in dubai Download ppt on ecotourism in india Ppt on water scarcity in california Download ppt on query processing and optimization