1.6.1 The
following steps are used to build a cobweb diagram. Follow them for the
given discrete-time dynamical system based on bacterial populations.
a. Graph the updating function.
b. Use your graph of the updating function to find the point ...
c. Reflect it off the diagonal to find the point ...
d. Use the graph of the updating function to find ...
e. Reflect off the diagonal to find the point ...
f. Use the graph of the updating function to find ... g. Sketch the solution as a function of time. The discrete-time dynamical system ...with ... = 1.0.
Get solution
1.6.2 The
following steps are used to build a cobweb diagram. Follow them for the
given discrete-time dynamical system based on bacterial populations.
a. Graph the updating function.
b. Use your graph of the updating function to find the point ...
c. Reflect it off the diagonal to find the point ...
d. Use the graph of the updating function to find ...
e. Reflect off the diagonal to find the point ...
f. Use the graph of the updating function to find ... g. Sketch the solution as a function of time. The discrete-time dynamical system ...= 0.5nt with ... =1.0.
Get solution
1.6.3 Cobweb
the following discrete-time dynamical systems for three steps starting
from the given initial condition. Compare with the solution found
earlier. ...
Get solution
1.6.4 Cobweb
the following discrete-time dynamical systems for three steps starting
from the given initial condition. Compare with the solution found
earlier. ...
Get solution
1.6.5 Cobweb
the following discrete-time dynamical systems for three steps starting
from the given initial condition. Compare with the solution found
earlier. ...
Get solution
1.6.6 Cobweb
the following discrete-time dynamical systems for three steps starting
from the given initial condition. Compare with the solution found
earlier. ...
Get solution
1.6.7 Graph
the updating functions associated with the following discrete-time
dynamical systems, and cobweb for five steps starting from the given
initial condition. ...
Get solution
1.6.8 Graph
the updating functions associated with the following discrete-time
dynamical systems, and cobweb for five steps starting from the given
initial condition. ...
Get solution
1.6.9 Graph
the updating functions associated with the following discrete-time
dynamical systems, and cobweb for five steps starting from the given
initial condition. ...
Get solution
1.6.10 Graph
the updating functions associated with the following discrete-time
dynamical systems, and cobweb for five steps starting from the given
initial condition. ...
Get solution
1.6.11 Graph
the updating functions associated with the following discrete-time
dynamical systems, and cobweb for five steps starting from the given
initial condition. ...
Get solution
1.6.12 Graph
the updating functions associated with the following discrete-time
dynamical systems, and cobweb for five steps starting from the given
initial condition. ...
Get solution
1.6.13 Find
the equilibria of the following discrete-time dynamical system from the
graphs of their updating functions Label the coordinates of the
equilibria. ...
Get solution
1.6.14 Find
the equilibria of the following discrete-time dynamical system from the
graphs of their updating functions Label the coordinates of the
equilibria. ...
Get solution
1.6.15 Find
the equilibria of the following discrete-time dynamical system from the
graphs of their updating functions Label the coordinates of the
equilibria. ...
Get solution
1.6.16 Find
the equilibria of the following discrete-time dynamical system from the
graphs of their updating functions Label the coordinates of the
equilibria. ...
Get solution
1.6.17 Sketch
graphs of the following updating functions over the given range and
mark the equilibria. Find the equilibria algebraically if possible f ( x )= ... for 0≤ x ≤2.
Get solution
1.6.18 Sketch
graphs of the following updating functions over the given range and
mark the equilibria. Find the equilibria algebraically if possible g ( y )= ... − 1 for 0≤ y ≤2.
Get solution
1.6.19 Graph
the following discrete-time dynamical systems. Solve for the equilibria
algebraically, and identify equilibria and the regions where the
updating function lies above the diagonal on your graph. ...
Get solution
1.6.20 Graph
the following discrete-time dynamical systems. Solve for the equilibria
algebraically, and identify equilibria and the regions where the
updating function lies above the diagonal on your graph. ...
Get solution
1.6.21 Graph
the following discrete-time dynamical systems. Solve for the equilibria
algebraically, and identify equilibria and the regions where the
updating function lies above the diagonal on your graph. ...
Get solution
1.6.22 Graph
the following discrete-time dynamical systems. Solve for the equilibria
algebraically, and identify equilibria and the regions where the
updating function lies above the diagonal on your graph. ...
Get solution
1.6.23 Find
the equilibria of the following discrete-time dynamical systems.
Compare with the results of your cobweb diagram from the earlier
problem. ... (as in Section 1.5, Exercise 5). Compose
the updating function associated with each discrete-time dynamical
system with itsel
f. Find the two-step discrete-time dynamical system.
Check that the result of applying the original discrete-time dynamical
system twice to the given initial condition matches the result of
applying the new discretetime dynamical system to the given initial
condition once. Volume follows ...
Get solution
1.6.24 Find
the equilibria of the following discrete-time dynamical systems.
Compare with the results of your cobweb diagram from the earlier
problem. ... (as in Section 1.5, Exercise 6). Section 1.5, Exercise 6 Compose
the updating function associated with each discrete-time dynamical
system with itsel
f. Find the two-step discrete-time dynamical system.
Check that the result of applying the original discrete-time dynamical
system twice to the given initial condition matches the result of
applying the new discretetime dynamical system to the given initial
condition once. Length obeys ...
Get solution
1.6.25 Find
the equilibria of the following discrete-time dynamical systems.
Compare with the results of your cobweb diagram from the earlier
problem. ...
Get solution
1.6.26 Find
the equilibria of the following discrete-time dynamical systems.
Compare with the results of your cobweb diagram from the earlier
problem. ... Exercise 8 Graph
the updating functions associated with the following discrete-time
dynamical systems, and cobweb for five steps starting from the given
initial condition. ...
Get solution
1.6.27 Find
the equilibria of the following discrete-time dynamical systems.
Compare with the results of your cobweb diagram from the earlier
problem. ... Exercise 9Graph
the updating functions associated with the following discrete-time
dynamical systems, and cobweb for five steps starting from the given
initial condition. ...
Get solution
1.6.28 Find
the equilibria of the following discrete-time dynamical systems.
Compare with the results of your cobweb diagram from the earlier
problem. ... Exercise 10 Graph
the updating functions associated with the following discrete-time
dynamical systems, and cobweb for five steps starting from the given
initial condition. ...
Get solution
1.6.29 Find
the equilibria of the following discrete-time dynamical systems.
Compare with the results of your cobweb diagram from the earlier
problem. ... Exercise 11 Graph
the updating functions associated with the following discrete-time
dynamical systems, and cobweb for five steps starting from the given
initial condition. ...
Get solution
1.6.30 Find
the equilibria of the following discrete-time dynamical systems.
Compare with the results of your cobweb diagram from the earlier
problem. ... Exercise 12) Graph
the updating functions associated with the following discrete-time
dynamical systems, and cobweb for five steps starting from the given
initial condition. ...
Get solution
1.6.31 Find
the equilibria of the following discrete-time dynamical systems that
include parameters. Identify values of the parameter for which there is
no equilibrium, for which the equilibrium is negative, and for which
there is more than one equilibrium. ...
Get solution
1.6.32 Find
the equilibria of the following discrete-time dynamical systems that
include parameters. Identify values of the parameter for which there is
no equilibrium, for which the equilibrium is negative, and for which
there is more than one equilibrium. ...
Get solution
1.6.33 Find
the equilibria of the following discrete-time dynamical systems that
include parameters. Identify values of the parameter for which there is
no equilibrium, for which the equilibrium is negative, and for which
there is more than one equilibrium. ...
Get solution
1.6.34 Find
the equilibria of the following discrete-time dynamical systems that
include parameters. Identify values of the parameter for which there is
no equilibrium, for which the equilibrium is negative, and for which
there is more than one equilibrium. ...
Get solution
1.6.35
Cobweb the following discrete-time dynamical systems for five steps
starting from the given initial condition. An alternative tree growth
discrete-time dynamical system with form ...with initial condition ... =10.
Get solution
1.6.36
Cobweb the following discrete-time dynamical systems for five steps
starting from the given initial condition. The lizard-mite system
(Example 1.5.3) ...with initial condition ... =0.
Get solution
1.6.37
Cobweb the following discrete-time dynamical systems for five steps
starting from the given initial condition. The model defined in Section
1.5, Exercise 37 starting from an initial volume of 1420. Section
1.5, Exercise 37 The following tables display data from four
experiments:
a. Cell volume after 10 minutes in a watery bath
b. Fish mass after 1 week in a chilly tank
c. Gnat population size after 3 days without food d.
Yield of several varieties of soybean before and after fertilization
For each, graph the new value as a function of the initial value, write
the discrete-time dynamical system, and fill in the missing value in the
table. ...
Get solution
1.6.38
Cobweb the following discrete-time dynamical systems for five steps
starting from the given initial condition. The model defined in Section
1.5, Exercise 38 starting from an initial mass of 13.1. Section 1.5,
Exercise 38 The following tables display data from four experiments:
a. Cell volume after 10 minutes in a watery bath
b. Fish mass after 1 week in a chilly tank
c. Gnat population size after 3 days without food d.
Yield of several varieties of soybean before and after fertilization
For each, graph the new value as a function of the initial value, write
the discrete-time dynamical system, and fill in the missing value in the
table. ...
Get solution
1.6.39
Cobweb the following discrete-time dynamical systems for five steps
starting from the given initial condition. The model defined in Section
1.5, Exercise 39 starting from an initial population of 800. Section
1.5, Exercise 39 The following tables display data from four
experiments:
a. Cell volume after 10 minutes in a watery bath
b. Fish mass after 1 week in a chilly tank
c. Gnat population size after 3 days without food d.
Yield of several varieties of soybean before and after fertilization
For each, graph the new value as a function of the initial value, write
the discrete-time dynamical system, and fill in the missing value in the
table. ...
Get solution
1.6.40
Cobweb the following discrete-time dynamical systems for five steps
starting from the given initial condition. The model defined in Section
1.5, Exercise 40 starting from an initial yield of 20. Section 1.5,
Exercise 40 The following tables display data from four experiments:
a. Cell volume after 10 minutes in a watery bath
b. Fish mass after 1 week in a chilly tank
c. Gnat population size after 3 days without food d.
Yield of several varieties of soybean before and after fertilization
For each, graph the new value as a function of the initial value, write
the discrete-time dynamical system, and fill in the missing value in the
table. ...
Get solution
1.6.41 Reconsider
the data describing the levels of a medication in the blood of two
patients over the course of several days (measured in mg per liter),
used in Section 1.5, Exercises 53 and 54. ... For
the first patient, graph the updating function and cobweb starting from
the initial condition on day 0. Find the equilibrium.
Get solution
1.6.42 Reconsider
the data describing the levels of a medication in the blood of two
patients over the course of several days (measured in mg per liter),
used in Section 1.5, Exercises 53 and 54. ... For
the second patient, graph the updating function and cobweb starting
from the initial condition on day 0. Find the equilibrium.
Get solution
1.6.43
Cobweb and find the equilibrium of the following discretetime
dynamical system. Consider a bacterial population that doubles every
hour, but 1.0×... individuals are removed after reproduction (Section 1.5, Exercise 57). Cobweb starting from ... = 3.0×... bacteria.
Get solution
1.6.45
Consider the following general models for bacterial populations with
harvest. Consider a bacterial population that doubles every hour, but h individuals are removed after reproduction. Find the equilibrium. Does it make sense?
Get solution
1.6.45
Consider the following general models for bacterial populations with
harvest. Consider a bacterial population that doubles every hour, but h individuals are removed after reproduction. Find the equilibrium. Does it make sense?
Get solution
1.6.46
Consider the following general models for bacterial populations with
harvest. Consider a bacterial population that increases by a
factor of r every hour, but 1.0×... individuals are removed after reproduction. Find the equilibrium. What values of r produce a positive equilibrium?
Get solution
1.6.47 Consider the general model ...for medication (Example 1.6.11). Find the loading dose (Example 1.6.7) in the following cases. α =0.2, S =2.
Get solution
1.6.48 Consider the general model ...for medication (Example 1.6.11). Find the loading dose (Example 1.6.7) in the following cases. α =0.8, S =4.
Get solution
1.6.49 Use
your computer (it may have a special feature for this) to find and
graph the first 10 points on the solutions of the following
discrete-time dynamical systems. The first two describe populations with
reproduction and immigration of 100 individuals per generation, and the
last two describe populations that have 100 individuals harvested or
removed each generation. ... ...
e. What happens if you run the last one for 15 steps? What is wrong with the model?
Get solution
1.6.50 Compose the medication discrete-time dynamical system ...with
itself 10 times. Plot the resulting function. Use this composition to
find the concentration after 10 days starting from concentrations of
1.0, 5.0, and 18.0 milligrams per liter. If the goal is to reach a
stable concentration of 2.0 milligrams per liter, do you think this is a
good therapy?
Get solution
