Modeling the Dynamics of Life: Calculus and Probability for Life Scientists
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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Concept explainers

Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
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Textbook Question
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Chapter 1.2, Problem 32E

Graph each of the following functions and its inverse. Mark the given point on the graph of each function.

  F ( y ) = y 2 + 1 for y ≥ 0. Mark the point ( 1 , F ( 1 ) ) on the graphs of F and F − 1 (based on Exercise 28 ).

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Chapter 1 Solutions

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists

Ch. 1.2 - Identify the variables and parameters in the...Ch. 1.2 - Prob. 2ECh. 1.2 - Compute the values of the following functions at...Ch. 1.2 - Compute the values of the following functions at...Ch. 1.2 - Compute the values of the following functions at...Ch. 1.2 - Compute the values of the following functions at...Ch. 1.2 - Graph the given points and say which point does...Ch. 1.2 - Graph the given points and say which point does...Ch. 1.2 - Graph the given points and say which point does...Ch. 1.2 - Graph the given points and say which point does...
Ch. 1.2 - Evaluate the following functions at the given...Ch. 1.2 - Evaluate the following functions at the given...Ch. 1.2 - Prob. 13ECh. 1.2 - Prob. 14ECh. 1.2 - Prob. 15ECh. 1.2 - Prob. 16ECh. 1.2 - Prob. 17ECh. 1.2 - Prob. 18ECh. 1.2 - Prob. 19ECh. 1.2 - Prob. 20ECh. 1.2 - Prob. 21ECh. 1.2 - Prob. 22ECh. 1.2 - Prob. 23ECh. 1.2 - Prob. 24ECh. 1.2 - Prob. 25ECh. 1.2 - Find the inverses of each of the following...Ch. 1.2 - Prob. 27ECh. 1.2 - Prob. 28ECh. 1.2 - Prob. 29ECh. 1.2 - Graph each of the following functions and its...Ch. 1.2 - Graph each of the following functions and its...Ch. 1.2 - Graph each of the following functions and its...Ch. 1.2 - Prob. 33ECh. 1.2 - Find the compositions of the given functions....Ch. 1.2 - Prob. 35ECh. 1.2 - Prob. 36ECh. 1.2 - Prob. 37ECh. 1.2 - Prob. 38ECh. 1.2 - Prob. 39ECh. 1.2 - Prob. 40ECh. 1.2 - Prob. 41ECh. 1.2 - Prob. 42ECh. 1.2 - Prob. 43ECh. 1.2 - Prob. 44ECh. 1.2 - Prob. 45ECh. 1.2 - Prob. 46ECh. 1.2 - Prob. 47ECh. 1.2 - Prob. 48ECh. 1.2 - Prob. 49ECh. 1.2 - Prob. 50ECh. 1.2 - Prob. 51ECh. 1.2 - Prob. 52ECh. 1.2 - The following series of functional compositions...Ch. 1.2 - The following series of functional compositions...Ch. 1.2 - The following series of functional compositions...Ch. 1.2 - Prob. 56ECh. 1.2 - Prob. 57ECh. 1.2 - Prob. 58ECh. 1.2 - Prob. 59ECh. 1.2 - Prob. 60ECh. 1.2 - Prob. 61ECh. 1.2 - Prob. 62ECh. 1.2 - Prob. 63ECh. 1.2 - Prob. 64ECh. 1.2 - Prob. 65ECh. 1.2 - Prob. 66ECh. 1.2 - Prob. 67ECh. 1.2 - Prob. 68ECh. 1.2 - Prob. 69ECh. 1.2 - Prob. 70ECh. 1.3 - Prob. 1ECh. 1.3 - Prob. 2ECh. 1.3 - Prob. 3ECh. 1.3 - Prob. 4ECh. 1.3 - Prob. 5ECh. 1.3 - Prob. 6ECh. 1.3 - Prob. 7ECh. 1.3 - Prob. 8ECh. 1.3 - Prob. 9ECh. 1.3 - Prob. 10ECh. 1.3 - Prob. 11ECh. 1.3 - Prob. 12ECh. 1.3 - Prob. 13ECh. 1.3 - Prob. 14ECh. 1.3 - Prob. 15ECh. 1.3 - Prob. 16ECh. 1.3 - Prob. 17ECh. 1.3 - Prob. 18ECh. 1.3 - Prob. 19ECh. 1.3 - Prob. 20ECh. 1.3 - Prob. 21ECh. 1.3 - Prob. 22ECh. 1.3 - Prob. 23ECh. 1.3 - Prob. 24ECh. 1.3 - Prob. 25ECh. 1.3 - Prob. 26ECh. 1.3 - Prob. 27ECh. 1.3 - Prob. 28ECh. 1.3 - Prob. 29ECh. 1.3 - Prob. 30ECh. 1.3 - Prob. 31ECh. 1.3 - Prob. 32ECh. 1.3 - Find the mass in kilograms of the following...Ch. 1.3 - Prob. 34ECh. 1.3 - Change the units in the following functions, and...Ch. 1.3 - Prob. 36ECh. 1.3 - Prob. 37ECh. 1.3 - Prob. 38ECh. 1.3 - Prob. 39ECh. 1.3 - Prob. 40ECh. 1.3 - Prob. 41ECh. 1.3 - Prob. 42ECh. 1.3 - Prob. 43ECh. 1.3 - Prob. 44ECh. 1.3 - Prob. 45ECh. 1.3 - Prob. 46ECh. 1.3 - Prob. 47ECh. 1.3 - Prob. 48ECh. 1.3 - Prob. 49ECh. 1.3 - Prob. 50ECh. 1.4 - For the following lines, find the slopes between...Ch. 1.4 - Prob. 2ECh. 1.4 - Prob. 3ECh. 1.4 - Prob. 4ECh. 1.4 - Prob. 5ECh. 1.4 - Prob. 6ECh. 1.4 - Prob. 7ECh. 1.4 - Prob. 8ECh. 1.4 - Prob. 9ECh. 1.4 - Prob. 10ECh. 1.4 - Prob. 11ECh. 1.4 - Prob. 12ECh. 1.4 - Prob. 13ECh. 1.4 - Prob. 14ECh. 1.4 - Prob. 15ECh. 1.4 - Prob. 16ECh. 1.4 - Prob. 17ECh. 1.4 - Prob. 18ECh. 1.4 - Prob. 19ECh. 1.4 - Prob. 20ECh. 1.4 - Prob. 21ECh. 1.4 - Prob. 22ECh. 1.4 - Prob. 23ECh. 1.4 - Prob. 24ECh. 1.4 - Prob. 25ECh. 1.4 - Prob. 26ECh. 1.4 - Prob. 27ECh. 1.4 - Prob. 28ECh. 1.4 - Prob. 29ECh. 1.4 - Prob. 30ECh. 1.4 - Prob. 31ECh. 1.4 - Prob. 32ECh. 1.4 - Prob. 33ECh. 1.4 - Prob. 34ECh. 1.4 - Prob. 35ECh. 1.4 - Prob. 36ECh. 1.4 - Prob. 37ECh. 1.4 - Prob. 38ECh. 1.4 - Prob. 39ECh. 1.4 - Prob. 40ECh. 1.4 - Prob. 41ECh. 1.4 - Prob. 42ECh. 1.4 - The following data give the elevation of the...Ch. 1.4 - Prob. 44ECh. 1.4 - Prob. 45ECh. 1.4 - Prob. 46ECh. 1.4 - Prob. 47ECh. 1.4 - Prob. 48ECh. 1.4 - Prob. 49ECh. 1.4 - Prob. 50ECh. 1.4 - Prob. 51ECh. 1.4 - Prob. 52ECh. 1.4 - Prob. 53ECh. 1.4 - Prob. 54ECh. 1.4 - Prob. 55ECh. 1.4 - Prob. 56ECh. 1.4 - Prob. 57ECh. 1.4 - Prob. 58ECh. 1.4 - Prob. 59ECh. 1.4 - Prob. 60ECh. 1.5 - Write the updating function associated with each...Ch. 1.5 - Write the updating function associated with each...Ch. 1.5 - Write the updating function associated with each...Ch. 1.5 - Write the updating function associated with each...Ch. 1.5 - Compose the updating function associated with each...Ch. 1.5 - Compose the updating function associated with each...Ch. 1.5 - Prob. 7ECh. 1.5 - Prob. 8ECh. 1.5 - Prob. 9ECh. 1.5 - Prob. 10ECh. 1.5 - Prob. 11ECh. 1.5 - Prob. 12ECh. 1.5 - Prob. 13ECh. 1.5 - Prob. 14ECh. 1.5 - Prob. 15ECh. 1.5 - Prob. 16ECh. 1.5 - Prob. 17ECh. 1.5 - Prob. 18ECh. 1.5 - Prob. 19ECh. 1.5 - Prob. 20ECh. 1.5 - Prob. 21ECh. 1.5 - Prob. 22ECh. 1.5 - Prob. 23ECh. 1.5 - Prob. 24ECh. 1.5 - Prob. 25ECh. 1.5 - Prob. 26ECh. 1.5 - Prob. 27ECh. 1.5 - Prob. 28ECh. 1.5 - Prob. 29ECh. 1.5 - Prob. 30ECh. 1.5 - Use the formula for the solution to find the...Ch. 1.5 - Prob. 32ECh. 1.5 - Prob. 33ECh. 1.5 - Prob. 34ECh. 1.5 - Prob. 35ECh. 1.5 - Prob. 36ECh. 1.5 - Prob. 37ECh. 1.5 - Prob. 38ECh. 1.5 - Prob. 39ECh. 1.5 - Prob. 40ECh. 1.5 - Prob. 41ECh. 1.5 - Prob. 42ECh. 1.5 - Prob. 43ECh. 1.5 - Prob. 44ECh. 1.5 - Prob. 45ECh. 1.5 - Prob. 46ECh. 1.5 - Prob. 47ECh. 1.5 - Prob. 48ECh. 1.5 - Prob. 49ECh. 1.5 - Prob. 50ECh. 1.5 - Prob. 51ECh. 1.5 - Prob. 52ECh. 1.5 - Prob. 53ECh. 1.5 - Prob. 54ECh. 1.5 - Prob. 55ECh. 1.5 - Prob. 56ECh. 1.5 - Prob. 57ECh. 1.5 - Prob. 58ECh. 1.5 - Prob. 59ECh. 1.5 - Prob. 60ECh. 1.5 - Prob. 61ECh. 1.5 - Prob. 62ECh. 1.6 - The following steps are used to build a cobweb...Ch. 1.6 - Prob. 2ECh. 1.6 - Prob. 3ECh. 1.6 - Prob. 4ECh. 1.6 - Prob. 5ECh. 1.6 - Prob. 6ECh. 1.6 - Prob. 7ECh. 1.6 - Prob. 8ECh. 1.6 - Prob. 9ECh. 1.6 - Prob. 10ECh. 1.6 - Prob. 11ECh. 1.6 - Prob. 12ECh. 1.6 - Prob. 13ECh. 1.6 - Find the equilibria of the following discrete-time...Ch. 1.6 - Prob. 15ECh. 1.6 - Prob. 16ECh. 1.6 - Prob. 17ECh. 1.6 - Prob. 18ECh. 1.6 - Prob. 19ECh. 1.6 - Prob. 20ECh. 1.6 - Prob. 21ECh. 1.6 - Prob. 22ECh. 1.6 - Prob. 23ECh. 1.6 - Prob. 24ECh. 1.6 - Prob. 25ECh. 1.6 - Prob. 26ECh. 1.6 - Prob. 27ECh. 1.6 - Prob. 28ECh. 1.6 - Prob. 29ECh. 1.6 - Prob. 30ECh. 1.6 - Prob. 31ECh. 1.6 - Prob. 32ECh. 1.6 - Prob. 33ECh. 1.6 - Prob. 34ECh. 1.6 - Prob. 35ECh. 1.6 - Prob. 36ECh. 1.6 - Prob. 37ECh. 1.6 - Prob. 38ECh. 1.6 - Prob. 39ECh. 1.6 - Prob. 40ECh. 1.6 - Prob. 41ECh. 1.6 - Prob. 42ECh. 1.6 - Cobweb and find the equilibrium of the following...Ch. 1.6 - Prob. 44ECh. 1.6 - Prob. 45ECh. 1.6 - Prob. 46ECh. 1.6 - Prob. 47ECh. 1.6 - Prob. 48ECh. 1.6 - Prob. 49ECh. 1.6 - Prob. 50ECh. 1.7 - Prob. 1ECh. 1.7 - Prob. 2ECh. 1.7 - Prob. 3ECh. 1.7 - Prob. 4ECh. 1.7 - Prob. 5ECh. 1.7 - Prob. 6ECh. 1.7 - Prob. 7ECh. 1.7 - Prob. 8ECh. 1.7 - Prob. 9ECh. 1.7 - Prob. 10ECh. 1.7 - Prob. 11ECh. 1.7 - Prob. 12ECh. 1.7 - Prob. 13ECh. 1.7 - Prob. 14ECh. 1.7 - Prob. 15ECh. 1.7 - Prob. 16ECh. 1.7 - Prob. 17ECh. 1.7 - Use the laws of logs to rewrite the following if...Ch. 1.7 - Prob. 19ECh. 1.7 - Prob. 20ECh. 1.7 - Prob. 21ECh. 1.7 - Prob. 22ECh. 1.7 - Prob. 23ECh. 1.7 - Prob. 24ECh. 1.7 - Prob. 25ECh. 1.7 - Prob. 26ECh. 1.7 - Prob. 27ECh. 1.7 - Prob. 28ECh. 1.7 - Prob. 29ECh. 1.7 - Prob. 30ECh. 1.7 - Prob. 31ECh. 1.7 - Prob. 32ECh. 1.7 - Prob. 33ECh. 1.7 - Prob. 34ECh. 1.7 - Prob. 35ECh. 1.7 - Prob. 36ECh. 1.7 - Prob. 37ECh. 1.7 - Prob. 38ECh. 1.7 - Prob. 39ECh. 1.7 - Prob. 40ECh. 1.7 - Prob. 41ECh. 1.7 - Prob. 42ECh. 1.7 - Prob. 43ECh. 1.7 - Prob. 44ECh. 1.7 - Prob. 45ECh. 1.7 - Prob. 46ECh. 1.7 - Prob. 47ECh. 1.7 - Prob. 48ECh. 1.7 - Prob. 49ECh. 1.7 - Prob. 50ECh. 1.7 - Prob. 51ECh. 1.7 - Prob. 52ECh. 1.7 - Prob. 53ECh. 1.7 - Prob. 54ECh. 1.7 - Prob. 55ECh. 1.7 - Prob. 56ECh. 1.7 - Prob. 57ECh. 1.7 - Prob. 58ECh. 1.7 - Prob. 59ECh. 1.7 - Prob. 60ECh. 1.7 - Prob. 61ECh. 1.7 - Prob. 62ECh. 1.7 - Prob. 63ECh. 1.7 - Prob. 64ECh. 1.7 - Prob. 65ECh. 1.7 - Prob. 66ECh. 1.7 - Prob. 67ECh. 1.7 - Prob. 68ECh. 1.7 - Prob. 69ECh. 1.7 - Prob. 70ECh. 1.7 - Prob. 71ECh. 1.7 - Prob. 72ECh. 1.7 - Prob. 73ECh. 1.8 - Prob. 1ECh. 1.8 - Prob. 2ECh. 1.8 - Prob. 3ECh. 1.8 - Prob. 4ECh. 1.8 - Prob. 5ECh. 1.8 - Prob. 6ECh. 1.8 - Prob. 7ECh. 1.8 - Prob. 8ECh. 1.8 - Prob. 9ECh. 1.8 - Prob. 10ECh. 1.8 - Prob. 11ECh. 1.8 - Prob. 12ECh. 1.8 - Prob. 13ECh. 1.8 - Prob. 14ECh. 1.8 - Prob. 15ECh. 1.8 - Prob. 16ECh. 1.8 - Prob. 17ECh. 1.8 - Prob. 18ECh. 1.8 - Prob. 19ECh. 1.8 - Prob. 20ECh. 1.8 - Prob. 21ECh. 1.8 - Prob. 22ECh. 1.8 - Prob. 23ECh. 1.8 - Prob. 24ECh. 1.8 - Prob. 25ECh. 1.8 - Prob. 26ECh. 1.8 - Prob. 27ECh. 1.8 - Prob. 28ECh. 1.8 - Prob. 29ECh. 1.8 - Prob. 30ECh. 1.8 - Prob. 31ECh. 1.8 - Prob. 32ECh. 1.8 - Prob. 33ECh. 1.8 - Prob. 34ECh. 1.8 - Prob. 35ECh. 1.8 - Prob. 36ECh. 1.8 - Prob. 37ECh. 1.8 - Prob. 38ECh. 1.8 - Prob. 39ECh. 1.8 - Prob. 40ECh. 1.8 - Prob. 41ECh. 1.8 - Prob. 42ECh. 1.8 - Prob. 43ECh. 1.8 - Prob. 44ECh. 1.8 - Prob. 45ECh. 1.8 - Prob. 46ECh. 1.8 - Prob. 47ECh. 1.8 - Prob. 48ECh. 1.8 - Prob. 49ECh. 1.8 - Prob. 50ECh. 1.8 - Prob. 51ECh. 1.9 - Prob. 1ECh. 1.9 - Prob. 2ECh. 1.9 - Prob. 3ECh. 1.9 - Prob. 4ECh. 1.9 - Prob. 5ECh. 1.9 - Prob. 6ECh. 1.9 - Prob. 7ECh. 1.9 - Prob. 8ECh. 1.9 - Prob. 9ECh. 1.9 - Prob. 10ECh. 1.9 - Prob. 11ECh. 1.9 - Prob. 12ECh. 1.9 - Prob. 13ECh. 1.9 - Prob. 14ECh. 1.9 - Prob. 15ECh. 1.9 - Prob. 16ECh. 1.9 - Prob. 17ECh. 1.9 - Prob. 18ECh. 1.9 - Prob. 19ECh. 1.9 - Prob. 20ECh. 1.9 - Prob. 21ECh. 1.9 - Prob. 22ECh. 1.9 - Prob. 23ECh. 1.9 - Prob. 24ECh. 1.9 - Prob. 25ECh. 1.9 - Prob. 26ECh. 1.9 - Prob. 27ECh. 1.9 - Prob. 28ECh. 1.9 - Prob. 29ECh. 1.9 - Prob. 30ECh. 1.9 - Prob. 31ECh. 1.9 - Prob. 32ECh. 1.9 - Prob. 33ECh. 1.9 - Prob. 34ECh. 1.9 - Prob. 35ECh. 1.9 - Prob. 36ECh. 1.9 - Prob. 37ECh. 1.9 - Prob. 38ECh. 1.9 - Prob. 39ECh. 1.9 - Prob. 40ECh. 1.9 - Prob. 41ECh. 1.9 - Prob. 42ECh. 1.9 - Prob. 43ECh. 1.9 - Prob. 44ECh. 1.9 - Prob. 45ECh. 1.9 - Prob. 46ECh. 1.9 - Prob. 47ECh. 1.9 - Prob. 48ECh. 1.9 - Prob. 49ECh. 1.9 - Prob. 50ECh. 1.9 - Prob. 51ECh. 1.10 - A population consists of 200 red birds and 800...Ch. 1.10 - A population consists of 200 red birds and 800...Ch. 1.10 - A population consists of 200 red birds and 800...Ch. 1.10 - Prob. 4ECh. 1.10 - Prob. 5ECh. 1.10 - Prob. 6ECh. 1.10 - Prob. 7ECh. 1.10 - Prob. 8ECh. 1.10 - Prob. 9ECh. 1.10 - Prob. 10ECh. 1.10 - Prob. 11ECh. 1.10 - Prob. 12ECh. 1.10 - Prob. 13ECh. 1.10 - Prob. 14ECh. 1.10 - Prob. 15ECh. 1.10 - Prob. 16ECh. 1.10 - Prob. 17ECh. 1.10 - Prob. 18ECh. 1.10 - Prob. 19ECh. 1.10 - Prob. 20ECh. 1.10 - Prob. 21ECh. 1.10 - Prob. 22ECh. 1.10 - Prob. 23ECh. 1.10 - Prob. 24ECh. 1.10 - Prob. 25ECh. 1.10 - Prob. 26ECh. 1.10 - Prob. 27ECh. 1.10 - Prob. 28ECh. 1.10 - Prob. 29ECh. 1.10 - Prob. 30ECh. 1.10 - Prob. 31ECh. 1.10 - Prob. 32ECh. 1.10 - Prob. 33ECh. 1.10 - Prob. 34ECh. 1.10 - Prob. 35ECh. 1.10 - The model of selection studied in this section is...Ch. 1.10 - Prob. 37ECh. 1.10 - Prob. 38ECh. 1.10 - Prob. 39ECh. 1.10 - Prob. 40ECh. 1.10 - Prob. 41ECh. 1.10 - Prob. 42ECh. 1.10 - Prob. 43ECh. 1.10 - Prob. 44ECh. 1.10 - Prob. 45ECh. 1.10 - Prob. 46ECh. 1.10 - Prob. 47ECh. 1.10 - Prob. 48ECh. 1.10 - Prob. 49ECh. 1.11 - Prob. 1ECh. 1.11 - Prob. 2ECh. 1.11 - Prob. 3ECh. 1.11 - Prob. 4ECh. 1.11 - Prob. 5ECh. 1.11 - Prob. 6ECh. 1.11 - Prob. 7ECh. 1.11 - Prob. 8ECh. 1.11 - Prob. 9ECh. 1.11 - Prob. 10ECh. 1.11 - Prob. 11ECh. 1.11 - Prob. 12ECh. 1.11 - Prob. 13ECh. 1.11 - Prob. 14ECh. 1.11 - Prob. 15ECh. 1.11 - Prob. 16ECh. 1.11 - Prob. 17ECh. 1.11 - Prob. 18ECh. 1.11 - Prob. 19ECh. 1.11 - Prob. 20ECh. 1 - Suppose you have a culture of bacteria, where the...Ch. 1 - Prob. 2SPCh. 1 - Prob. 3SPCh. 1 - A lab has a culture of a new kind of bacteria...Ch. 1 - Prob. 5SPCh. 1 - Prob. 6SPCh. 1 - Prob. 7SPCh. 1 - Prob. 8SPCh. 1 - Prob. 9SPCh. 1 - Prob. 10SPCh. 1 - A person develops a small liver tumor. It grows...Ch. 1 - Prob. 12SPCh. 1 - Prob. 13SPCh. 1 - Prob. 14SPCh. 1 - Prob. 15SPCh. 1 - Prob. 16SPCh. 1 - Prob. 17SPCh. 1 - Prob. 18SPCh. 1 - Prob. 19SPCh. 1 - Prob. 20SPCh. 1 - Prob. 21SPCh. 1 - Prob. 22SPCh. 1 - Prob. 23SPCh. 1 - Prob. 24SPCh. 1 - Prob. 25SPCh. 1 - Prob. 26SPCh. 1 - Prob. 27SPCh. 1 - Prob. 28SPCh. 1 - Prob. 29SP
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