Modeling the Dynamics of Life: Calculus and Probability for Life Scientists
3rd Edition
ISBN: 9780840064189
Author: Frederick R. Adler
Publisher: Cengage Learning
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Chapter 2.1, Problem 24E
a
To determine
To calculate: To find the average rate of change between times 0 and 1.0 from the population size.
a
Expert Solution
Answer to Problem 24E
The average rate of change between times 0 and 1 is
Explanation of Solution
Given information:
Calculation:
Consider the following equation for a population size.
The population at time t=0 is
The population at time t= 0.1 is as follows:
The population at time t=0.01 is
The population at time t=0.001 is shown below:
For a given formula, the average rate of change between times
The average rate of change between times 0 and 1 is
b
To determine
To calculate: To find the average rate of change between times 0 and 0.1 from the population size.
b
Expert Solution
Answer to Problem 24E
The average rate of change between times 0 and 0.1 is
Explanation of Solution
Given information:
Calculation:
The average rate of change between times 0 and 0.1 is as follows:
c
To determine
To calculate: To find the average rate of change between times 0 and 0.01 from the population size.
c
Expert Solution
Answer to Problem 24E
The average rate of change between times 0 and 0.01 is
Explanation of Solution
Given information:
Calculation:
The average rate of change between times 0 and 0.01 is
d
To determine
To calculate: To find the average rate of change between times 0 and 0.001 from the population size.
d
Expert Solution
Answer to Problem 24E
The average rate of change between times 0 and 0.001 is
Explanation of Solution
Given information:
Calculation:
The average rate of change between times 0 and 0.001 is shown below:
e
To determine
To calculate: To find the limit using the obtained values
e
Expert Solution
Answer to Problem 24E
The limit is 0.693.
Explanation of Solution
Given information:
Calculation:
The limit is 0.693.
f
To determine
To calculate: To graph the tangent line using the obtained values
f
Expert Solution
Answer to Problem 24E
Hence the graph is drawn and the equation of the tangent line is
Explanation of Solution
Given information:
Calculation:
Since the limit is 0.693, then the slope of the tangent is 0.693
The equation of the tangent line is
ββ
The graph of the tangent line is shown below:
ββ
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Chapter 2 Solutions
Modeling the Dynamics of Life: Calculus and Probability for Life Scientists
Ch. 2.1 - Prob. 1ECh. 2.1 - Prob. 2ECh. 2.1 - Prob. 3ECh. 2.1 - Prob. 4ECh. 2.1 - Prob. 5ECh. 2.1 - Prob. 6ECh. 2.1 - Prob. 7ECh. 2.1 - Prob. 8ECh. 2.1 - Prob. 9ECh. 2.1 - Prob. 10E
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Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Learn Algebra 6 : Rate of Change; Author: Derek Banas;https://www.youtube.com/watch?v=Dw701mKcJ1k;License: Standard YouTube License, CC-BY