Download presentation

Presentation is loading. Please wait.

Published byCole Decourcey Modified over 3 years ago

1
Exponential Applications Exponential Growth and Decay Models

2
8/14/2013 Exponential Applications 2 Exponential Functions Increasing and Decreasing Exponential growth : f(x) = C a x for a > 1 and C > 0 Example : f(x) = C2 x Exponential decay : x y f(x) = C2 x (0, C) Domain = R Range = { x x > 0 } Exponential Growth Exponential Compounding

3
8/14/2013 Exponential Applications 3 Exponential Functions Increasing and Decreasing Exponential growth : f(x) = C a x Exponential decay : g(x) = f(–x) = C a –x for a > 1... a reflection of f(x) h(x) = Cb x x y f(x) = C2 x g(x) = f(–x) (0, C) Domain = R Range = { x x > 0 } OR 1 a b =b =, say a = 2, for 0 < b < 1 and = C2 –x h(x) = C ( ) 1 2 x Exponential Decay

4
8/14/2013 Exponential Applications 4 Exponential Functions Increasing and Decreasing Exponential growth : f(x) = C a x Exponential decay : g(x) = f(–x) = C a –x x y f(x) = C2 x g(x) = f(–x) (0, C) Domain = R Range = { x x > 0 } = C2 –x Questions: Intercepts ? Asymptotes ? Growth factor a ? Decay factor a ? One a > 1 0 < a < 1 Exponential Growth Exponential Decay Exponential Compounding

5
8/14/2013 Exponential Applications 5 Exponential Functions Increasing and Decreasing Exponential growth : f(x) = C a x Exponential decay : g(x) = f(–x) = C a –x x y f(x) = C2 x g(x) = f(–x) (0, C) Domain = R Range = { x x > 0 } = C2 –x f = { (x, 2 x ) x R } g = { (x, 2 –x ) x R } As ordered pairs, with C = 1, and

6
8/14/2013 Exponential Applications 6 Exponential Functions Increasing and Decreasing Exponential growth : f(x) = C a x Exponential decay : g(x) = f(–x) = C a –x x y f(x) = C2 x g(x) = f(–x) (0, C) Domain = R Range = { x x > 0 } = C2 –x In tabular form, with C = 1, –2 ¼ 4 –1 ½ 2 011011 12½12½ 24¼24¼ 3 8 –3 8 x 2 x 2 –x 16 4 16 16 16 –4

7
8/14/2013 Exponential Applications 7 Think about it !

8
8/14/2013 Exponential Applications 8 Solving Equations: Examples 1. World population 195019601970198019902000 20102020203020402050 15 14 13 12 11 10 9 8 7 6 5 4 3 2 t P(t) 1950 2.5098 1960 3.0000 1970 3.5859 1980 4.2862 1990 5.1233 2000 6.1239 2010 7.3199 2020 8.7495 2030 10.458 2040 12.500 2050 14.942 t P( t) P1P1 P2P2 P3P3 ( x 10 9 ) P(t) = 3(1.018) t–1960

9
8/14/2013 Exponential Applications 9 Spare Parts Slide 2 2 | | | ± ½ ½ ½ ¼ ¼ ¼

Similar presentations

OK

1 Copyright © 2010, Elsevier Inc. All rights Reserved Fig 2.1 Chapter 2.

1 Copyright © 2010, Elsevier Inc. All rights Reserved Fig 2.1 Chapter 2.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on db2 introduction to algebra Ppt on summary writing powerpoint Ppt on power grid failure 9-13-2015 Ppt on water resources for class 4 Ppt on mobile computing pdf Renal system anatomy and physiology ppt on cells Colon anatomy and physiology ppt on cells Ppt on file system in unix what is domain Ppt on mobile apps Ppt on different solid figures nets