Download presentation

Presentation is loading. Please wait.

Published byDevin Iams Modified over 2 years ago

1
Growth and Decay Exponential Models

2
Differs from polynomial functions. Polynomial Functions have exponents of whole numbers Exponential Functions have “x” as the exponent. Exponential Model: f(x) = a∙b x, a > 0, b > 0, and x is any real number There are two kinds of exponential models Growth Decay

3
Exponential Growth f(x) = a∙b x, where b > 1 Examples: f(x) = 5 x, g(x) = 2 ∙3 x Definition: as x increases so does f(x), and it increases very quickly. Graph:

4
Exponential Decay f(x) = a∙b x, where 0 < b < 1 Examples: f(x) = (1/2) x, g(x) = 3 ∙(3/5) x Definition: as x increases, f(x) decreases quickly, but never reaches zero. Graph:

5
Determine if the model is exponential growth or decay. 1. f(x) = 3 ∙2 x 2. g(x) = -5 ∙4 x 3. f(x) = 4 ∙(1/3) x 4. h(x) =.89 -x 5. g(x) = 7 -x 6. f(x) = (5/3) x

6
Determine if the graph is exponential growth, decay, or neither. 1. 2. 3.

7
Exponential Growth vs. Decay GROWTHDECAY

8
Horizontal Asymptote Both, exponential growth & decay, have a horizontal asymptote. A horizontal asymptote is the line that f(x) approaches as x approaches positive of negative infinity. It also is the lower boundary of the range for the exponential functions.

9
Identify the horizontal asymptote, domain, and range of the function. 1. f(x) = 2 x 2. h(x) = (2/3) x 3. f(x) = 4 (x+1) 4. f(x) = 5 x + 3

10
Transformations Graph the following functions in your calculator. How to the graphs transform from f(x) to g(x)? f(x) = 2 x and g(x) = 2 x+1 How would f(x) transform to g(x)? f(x) = 2 x and g(x) = 2 x – 1 Summarize how you would describe the transformation of f(x) to g(x+a)?

11
Transformations cont. Graph the following functions in your calculator. How to the graphs transform from f(x) to g(x)? f(x) = 3 x and g(x) = 3 x + 1 How would f(x) transform to g(x)? f(x) = 3 x and g(x) = 3 x – 1 Summarize how you would describe the transformation of f(x) to g(x) + a.

12
Describe the transformation of f(x) to g(x). 1. f(x) = 4 x and g(x) = 4 x+5 2. f(x) = (1/3) x and g(x) = (1/3) x – 4 3. f(x) = 2∙8 x and g(x) = 2∙8 x-3 + 1 4. f(x) = 7 x+1 and g(x) = 7 x+3 – 6

Similar presentations

OK

Objective Write and evaluate exponential expressions to model growth and decay situations.

Objective Write and evaluate exponential expressions to model growth and decay situations.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on small and large scale industries in india Ppt on breast cancer treatment Ppt on contact and noncontact force Slides for ppt on internet Ppt on library management system using java Free ppt on uses of plants Ppt on iso 9000 and 14000 Mp ppt online viewer Volumetric 3d display ppt online Ppt on swami vivekananda speech