Explanation Given information: The function P = 15 e − 0.06 t Concept involved: The General Exponential Function: Exponential growth or decay is often described in terms of percent growth or decay rates. Exponential Growth: P = P 0 a t o r P = P 0 ( 1 + r ) t P 0 is called initial quantity or value (the amount before measuring growth) a = 1 + r is called the Growth factor ,The variable r is called Growth rate Or percent rate of change.For exponential growth factor a is always greater than one ( a > 1 ) and r is positive. t represents time (number of time intervals that have passed) Example: P = 10 ( 1.45 ) t Exponential Decay: P = P 0 a t o r P = P 0 ( 1 − r ) t P 0 is called initial quantity or value (the amount before measuring decay) a = 1 − r is called the Decay factor ,The variable r is called Decay rate Or percent rate of change.For exponential decay factor a is always in between 0 and 1 ( 0 < a < 1 ) and r is negative. t represents time (number of time intervals that have passed) Example: P = 10 ( 0.85 ) t The exponential e is used when modeling continuous growth that occurs naturally such as populations, bacteria, radioactive decay, etc. You can think of e like a universal constant representing how fast you could possibly grow using a continuous process. P = P 0 e k t (Note: for continuous growth or decay function a = e k ) Calculation: Steps Description P = 15 ︷ P 0 e − 0

6th Edition

ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 1.6, Problem 23P

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Whether given function represent exponential growth or decay, its initial quantity, growth rate, and state if the growth rate is continuous.

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Chapter 1.6, Problem 22P

Chapter 1.6, Problem 24P

Chapter 1 Solutions

APPLIED CALCULUS (WILEY PLUS)

Ch. 1.1 - Prob. 1P Ch. 1.1 - Prob. 2P Ch. 1.1 - Prob. 3P Ch. 1.1 - Prob. 4P Ch. 1.1 - Prob. 5P Ch. 1.1 - Prob. 6P Ch. 1.1 - Prob. 7P Ch. 1.1 - Prob. 8P Ch. 1.1 - Prob. 9P Ch. 1.1 - Prob. 10P

Ch. 1.1 - Prob. 11P Ch. 1.1 - Prob. 12P Ch. 1.1 - Prob. 13P Ch. 1.1 - Prob. 14P Ch. 1.1 - Prob. 15P Ch. 1.1 - Prob. 16P Ch. 1.1 - Prob. 17P Ch. 1.1 - Prob. 18P Ch. 1.1 - Prob. 19P Ch. 1.1 - Prob. 20P Ch. 1.1 - Prob. 21P Ch. 1.1 - Prob. 22P Ch. 1.1 - Prob. 23P Ch. 1.1 - Prob. 24P Ch. 1.1 - Prob. 25P Ch. 1.1 - Prob. 26P Ch. 1.1 - Prob. 27P Ch. 1.1 - Prob. 28P Ch. 1.1 - Prob. 29P Ch. 1.1 - Prob. 30P Ch. 1.1 - Prob. 31P Ch. 1.1 - Prob. 32P Ch. 1.1 - Prob. 33P Ch. 1.1 - Prob. 34P Ch. 1.1 - Prob. 35P Ch. 1.1 - Prob. 36P Ch. 1.1 - Prob. 37P Ch. 1.1 - Prob. 38P Ch. 1.1 - Prob. 39P Ch. 1.1 - Prob. 40P Ch. 1.2 - Prob. 1P Ch. 1.2 - Prob. 2P Ch. 1.2 - Prob. 3P Ch. 1.2 - Prob. 4P Ch. 1.2 - Prob. 5P Ch. 1.2 - Prob. 6P Ch. 1.2 - Prob. 7P Ch. 1.2 - Prob. 8P Ch. 1.2 - Prob. 9P Ch. 1.2 - Prob. 10P Ch. 1.2 - Prob. 11P Ch. 1.2 - Prob. 12P Ch. 1.2 - Prob. 13P Ch. 1.2 - Prob. 14P Ch. 1.2 - Prob. 15P Ch. 1.2 - Prob. 16P Ch. 1.2 - Prob. 17P Ch. 1.2 - Prob. 18P Ch. 1.2 - Prob. 19P Ch. 1.2 - Prob. 20P Ch. 1.2 - 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Whether given function represent exponential growth or decay, its initial quantity, growth rate, and state if the growth rate is continuous.

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Whether given function represent exponential growth or decay, its initial quantity, growth rate, and state if the growth rate is continuous.