Explanation Given information: In 1913, Carlson conducted the classic experiment in which he grew yeast, Saccharomyces cerevisiae, in laboratory cultures and collected data every hour for 18 hours. The following table shows the yeast population, P, at representative time t in hours. From the given information the yeast population, P ( t ) , is a function of time t in hours. The term P ′ ( t ) represents the first order derivative i.e. rate of change of yeast population. Average rate of change of yeast population = change in yeast population time period = Δ P Δ t For interval [ 0 , 2 ] ; Δ P Δ t = P ( 2 ) − P ( 0 ) 2 − 0 = 29.0 − 9.6 2 = 9.7 For interval [ 2 , 4 ] ; Δ P Δ t = P ( 4 ) − P ( 2 ) 4 − 2 = 71.1 − 29.0 2 = 21.05 For interval [ 4 , 6 ] ; Δ P Δ t = P ( 6 ) − P ( 4 ) 6 − 4 = 174.6 − 71.1 2 = 51.75 For interval [ 6 , 8 ] ; Δ P Δ t = P ( 8 ) − P ( 6 ) 8 − 6 = 350.7 − 174 To determine (b) To state: About the sign of d 2 P / d t 2 .

6th Edition

ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Question

Chapter 2.4, Problem 36P

To determine

(a)

To calculate:

The average rate of change of P per hour for the time intervals shown between 0 to 18 hours.

To determine

(b)

To state:

About the sign of d2P/dt2.

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Chapter 2.4, Problem 35P

Chapter 2.5, Problem 1P

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Chapter 2 Solutions

APPLIED CALCULUS (WILEY PLUS)

Ch. 2.1 - Prob. 1P Ch. 2.1 - Prob. 2P Ch. 2.1 - Prob. 3P Ch. 2.1 - Prob. 4P Ch. 2.1 - Prob. 5P Ch. 2.1 - Prob. 6P Ch. 2.1 - Prob. 7P Ch. 2.1 - Prob. 8P Ch. 2.1 - Prob. 9P Ch. 2.1 - Prob. 10P

Ch. 2.1 - Prob. 11P Ch. 2.1 - Prob. 12P Ch. 2.1 - Prob. 13P Ch. 2.1 - Prob. 14P Ch. 2.1 - Prob. 15P Ch. 2.1 - Prob. 16P Ch. 2.1 - Prob. 17P Ch. 2.1 - Prob. 18P Ch. 2.1 - Prob. 19P Ch. 2.1 - Prob. 20P Ch. 2.1 - Prob. 21P Ch. 2.1 - Prob. 22P Ch. 2.1 - Prob. 23P Ch. 2.1 - Prob. 24P Ch. 2.1 - Prob. 25P Ch. 2.1 - Prob. 26P Ch. 2.1 - Prob. 27P Ch. 2.1 - Prob. 28P Ch. 2.1 - Prob. 29P Ch. 2.1 - Prob. 30P Ch. 2.1 - Prob. 31P Ch. 2.1 - Prob. 32P Ch. 2.1 - Prob. 33P Ch. 2.1 - Prob. 34P Ch. 2.1 - Prob. 35P Ch. 2.1 - Prob. 36P Ch. 2.1 - Prob. 37P Ch. 2.1 - Prob. 38P Ch. 2.1 - Prob. 39P Ch. 2.1 - Prob. 40P Ch. 2.1 - Prob. 41P Ch. 2.2 - Prob. 1P Ch. 2.2 - Prob. 2P Ch. 2.2 - Prob. 3P Ch. 2.2 - Prob. 4P Ch. 2.2 - Prob. 5P Ch. 2.2 - Prob. 6P Ch. 2.2 - Prob. 7P Ch. 2.2 - Prob. 8P Ch. 2.2 - Prob. 9P Ch. 2.2 - Prob. 10P Ch. 2.2 - Prob. 11P Ch. 2.2 - Prob. 12P Ch. 2.2 - Prob. 13P Ch. 2.2 - Prob. 14P Ch. 2.2 - Prob. 15P Ch. 2.2 - Prob. 16P Ch. 2.2 - Prob. 17P Ch. 2.2 - Prob. 18P Ch. 2.2 - Prob. 19P Ch. 2.2 - 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Prob. 36P Ch. 2.3 - Prob. 37P Ch. 2.3 - Prob. 38P Ch. 2.3 - Prob. 39P Ch. 2.3 - Prob. 40P Ch. 2.3 - Prob. 41P Ch. 2.3 - Prob. 42P Ch. 2.3 - Prob. 43P Ch. 2.3 - Prob. 44P Ch. 2.3 - Prob. 45P Ch. 2.3 - Prob. 46P Ch. 2.3 - Prob. 47P Ch. 2.3 - Prob. 48P Ch. 2.3 - Prob. 49P Ch. 2.3 - Prob. 50P Ch. 2.3 - Prob. 51P Ch. 2.3 - Prob. 52P Ch. 2.3 - Prob. 53P Ch. 2.3 - Prob. 54P Ch. 2.3 - Prob. 55P Ch. 2.3 - Prob. 56P Ch. 2.3 - Prob. 57P Ch. 2.3 - Prob. 58P Ch. 2.3 - Prob. 59P Ch. 2.3 - Prob. 60P Ch. 2.3 - Prob. 61P Ch. 2.3 - Prob. 62P Ch. 2.3 - Prob. 63P Ch. 2.3 - Prob. 64P Ch. 2.3 - Prob. 65P Ch. 2.3 - Prob. 66P Ch. 2.3 - Prob. 67P Ch. 2.3 - Prob. 68P Ch. 2.3 - Prob. 69P Ch. 2.4 - Prob. 1P Ch. 2.4 - Prob. 2P Ch. 2.4 - Prob. 3P Ch. 2.4 - Prob. 4P Ch. 2.4 - Prob. 5P Ch. 2.4 - Prob. 6P Ch. 2.4 - Prob. 7P Ch. 2.4 - Prob. 8P Ch. 2.4 - Prob. 9P Ch. 2.4 - Prob. 10P Ch. 2.4 - Prob. 11P Ch. 2.4 - Prob. 12P Ch. 2.4 - Prob. 13P Ch. 2.4 - Prob. 14P Ch. 2.4 - Prob. 15P Ch. 2.4 - Prob. 16P Ch. 2.4 - Prob. 17P Ch. 2.4 - 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(a) To calculate: The average rate of change of P per hour for the time intervals shown between 0 to 18 hours.

Solution Summary: The author explains how Carlson conducted the classic experiment in which he grew yeast, Saccharomyces cerevisiae, in laboratory cultures and collected data every hour for 18 hours.