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: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

See similar textbooks

Concept explainers

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.

Videos

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.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 2.4, Problem 35P

Chapter 2.5, Problem 1P

Chapter 2 Solutions

EBK APPLIED CALCULUS, ENHANCED ETEXT

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 - Prob. 20P Ch. 2.2 - Prob. 21P Ch. 2.2 - Prob. 22P Ch. 2.2 - Prob. 23P Ch. 2.2 - Prob. 24P Ch. 2.2 - Prob. 25P Ch. 2.2 - Prob. 26P Ch. 2.2 - Prob. 27P Ch. 2.2 - Prob. 28P Ch. 2.2 - Prob. 29P Ch. 2.2 - Prob. 30P Ch. 2.2 - Prob. 31P Ch. 2.2 - Prob. 32P Ch. 2.2 - Prob. 33P Ch. 2.2 - Prob. 34P Ch. 2.2 - Prob. 35P Ch. 2.3 - Prob. 1P Ch. 2.3 - Prob. 2P Ch. 2.3 - Prob. 3P Ch. 2.3 - Prob. 4P Ch. 2.3 - Prob. 5P Ch. 2.3 - Prob. 6P Ch. 2.3 - Prob. 7P Ch. 2.3 - Prob. 8P Ch. 2.3 - Prob. 9P Ch. 2.3 - Prob. 10P Ch. 2.3 - Prob. 11P Ch. 2.3 - Prob. 12P Ch. 2.3 - Prob. 13P Ch. 2.3 - Prob. 14P Ch. 2.3 - Prob. 15P Ch. 2.3 - Prob. 16P Ch. 2.3 - Prob. 17P Ch. 2.3 - Prob. 18P Ch. 2.3 - Prob. 19P Ch. 2.3 - Prob. 20P Ch. 2.3 - Prob. 21P Ch. 2.3 - Prob. 22P Ch. 2.3 - Prob. 23P Ch. 2.3 - Prob. 24P Ch. 2.3 - Prob. 25P Ch. 2.3 - Prob. 26P Ch. 2.3 - Prob. 27P Ch. 2.3 - Prob. 28P Ch. 2.3 - Prob. 29P Ch. 2.3 - Prob. 30P Ch. 2.3 - Prob. 31P Ch. 2.3 - Prob. 32P Ch. 2.3 - Prob. 33P Ch. 2.3 - Prob. 34P Ch. 2.3 - Prob. 35P Ch. 2.3 - 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 - Prob. 18P Ch. 2.4 - Prob. 19P Ch. 2.4 - Prob. 20P Ch. 2.4 - Prob. 21P Ch. 2.4 - Prob. 22P Ch. 2.4 - Prob. 23P Ch. 2.4 - Prob. 24P Ch. 2.4 - Prob. 25P Ch. 2.4 - Prob. 26P Ch. 2.4 - Prob. 27P Ch. 2.4 - Prob. 28P Ch. 2.4 - Prob. 29P Ch. 2.4 - Prob. 30P Ch. 2.4 - Prob. 31P Ch. 2.4 - Prob. 32P Ch. 2.4 - Prob. 33P Ch. 2.4 - Prob. 34P Ch. 2.4 - Prob. 35P Ch. 2.4 - Prob. 36P Ch. 2.5 - Prob. 1P Ch. 2.5 - Prob. 2P Ch. 2.5 - Prob. 3P Ch. 2.5 - Prob. 4P Ch. 2.5 - Prob. 5P Ch. 2.5 - Prob. 6P Ch. 2.5 - Prob. 7P Ch. 2.5 - Prob. 8P Ch. 2.5 - Prob. 9P Ch. 2.5 - Prob. 10P Ch. 2.5 - Prob. 11P Ch. 2.5 - Prob. 12P Ch. 2.5 - Prob. 13P Ch. 2.5 - Prob. 14P Ch. 2.5 - Prob. 15P Ch. 2.5 - Prob. 16P Ch. 2.5 - Prob. 17P Ch. 2.5 - Prob. 18P Ch. 2.5 - Prob. 19P Ch. 2 - Prob. 1SYU Ch. 2 - Prob. 2SYU Ch. 2 - Prob. 3SYU Ch. 2 - Prob. 4SYU Ch. 2 - Prob. 5SYU Ch. 2 - Prob. 6SYU Ch. 2 - Prob. 7SYU Ch. 2 - Prob. 8SYU Ch. 2 - Prob. 9SYU Ch. 2 - Prob. 10SYU Ch. 2 - Prob. 11SYU Ch. 2 - Prob. 12SYU Ch. 2 - Prob. 13SYU Ch. 2 - Prob. 14SYU Ch. 2 - Prob. 15SYU Ch. 2 - Prob. 16SYU Ch. 2 - Prob. 17SYU Ch. 2 - Prob. 18SYU Ch. 2 - Prob. 19SYU Ch. 2 - Prob. 20SYU Ch. 2 - Prob. 21SYU Ch. 2 - Prob. 22SYU Ch. 2 - Prob. 23SYU Ch. 2 - Prob. 24SYU Ch. 2 - Prob. 25SYU Ch. 2 - Prob. 26SYU Ch. 2 - Prob. 27SYU Ch. 2 - Prob. 28SYU Ch. 2 - Prob. 29SYU Ch. 2 - Prob. 30SYU Ch. 2 - Prob. 31SYU Ch. 2 - Prob. 32SYU Ch. 2 - Prob. 33SYU Ch. 2 - Prob. 34SYU Ch. 2 - Prob. 35SYU Ch. 2 - Prob. 36SYU Ch. 2 - Prob. 37SYU Ch. 2 - Prob. 38SYU Ch. 2 - Prob. 39SYU Ch. 2 - Prob. 40SYU Ch. 2 - Prob. 41SYU Ch. 2 - Prob. 42SYU Ch. 2 - Prob. 43SYU Ch. 2 - Prob. 44SYU Ch. 2 - Prob. 45SYU Ch. 2 - Prob. 46SYU Ch. 2 - Prob. 47SYU Ch. 2 - Prob. 48SYU Ch. 2 - Prob. 49SYU Ch. 2 - Prob. 50SYU Ch. 2 - Prob. 51SYU Ch. 2 - Prob. 52SYU Ch. 2 - Prob. 53SYU Ch. 2 - Prob. 54SYU Ch. 2 - Prob. 55SYU Ch. 2 - Prob. 1FOT Ch. 2 - Prob. 2FOT Ch. 2 - Prob. 3FOT Ch. 2 - Prob. 4FOT Ch. 2 - Prob. 5FOT Ch. 2 - Prob. 6FOT Ch. 2 - Prob. 7FOT Ch. 2 - Prob. 8FOT Ch. 2 - Prob. 9FOT Ch. 2 - Prob. 10FOT Ch. 2 - Prob. 11FOT Ch. 2 - Prob. 12FOT Ch. 2 - Prob. 13FOT Ch. 2 - Prob. 14FOT Ch. 2 - Prob. 15FOT Ch. 2 - Prob. 16FOT Ch. 2 - Prob. 17FOT Ch. 2 - Prob. 18FOT Ch. 2 - Prob. 19FOT Ch. 2 - Prob. 20FOT Ch. 2 - Prob. 21FOT Ch. 2 - Prob. 22FOT Ch. 2 - Prob. 23FOT Ch. 2 - Prob. 24FOT Ch. 2 - Prob. 25FOT Ch. 2 - Prob. 26FOT Ch. 2 - Prob. 27FOT Ch. 2 - Prob. 28FOT Ch. 2 - Prob. 29FOT Ch. 2 - Prob. 30FOT Ch. 2 - Prob. 31FOT Ch. 2 - Prob. 32FOT Ch. 2 - Prob. 33FOT Ch. 2 - Prob. 34FOT Ch. 2 - Prob. 35FOT Ch. 2 - Prob. 36FOT Ch. 2 - Prob. 37FOT Ch. 2 - Prob. 38FOT Ch. 2 - Prob. 39FOT Ch. 2 - Prob. 40FOT Ch. 2 - Prob. 41FOT Ch. 2 - Prob. 42FOT Ch. 2 - Prob. 43FOT

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

(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.