Explanation Given information: The function P = 5 ( 1.05 ) 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 = 5 ︷ P 0 ( 1

6th Edition

ISBN: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Chapter 1.6, Problem 21P

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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 20P

Chapter 1.6, Problem 22P

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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

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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.