In a forest in Alberta, every year 85% of the population of red deer either die...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
In a forest in Alberta, every year 85% of the population of red deer either die of natural causes or are eaten by predators. In the meantime, there are 8 new red deer per square kilometer. The discrete-time dynamical system (DTDS) that gives the population of red deer per square kilometer each year is Pt+1 = 0.15pt + 8 (Can you justify why it is the DTDS?) a) If there are 16 red deer per square kilometer now, how many red deer per square kilometer will there be in three years? Give your answer as a decimal with an accuracy of two decimal places. Answer: 9.43 b) Give the updating function f of the dynamical system, written as a function of a variable . f(x) = .15*x+8 Find its inverse, also written as a function of a variable x, if it exists. Write none if the inverse function doesn't exist. -(x) = c) Determine the equilibrium point p* of this dynamical system. Give exact values, not decimals; for instance, 2; 7; 7/3. d) Find the general solution of the dynamical system (ie., a formula in terms of t) given the initial condition po = 16. Use exact values, not decimals. Pt = e) Graph the points of the solution of the discrete time dynamical system with po = 16 (four values in addition to the initial condition are enough). Click on the left button of your mouse to enter point of your graph. You can always adjust the coordinates of the last point that you have entered using the field with the coordinates and pressing the return key. Label for the horizontal axis of the graph below: O Pt+1 O x Ot O pt Oy Label for the vertical axis of the graph below: O Pt+1 O Pt Oy Ot Ox Label for the vertical axis of the graph below: O Pt+1 pt Ot Ox -1 16- 14- 12- 10- 8 6 4 2 0 Clear Coordinates 1 2 3 4 f) Draw the cobweb diagram of the dynamical system with po axis. Notice the axes may not start at zero in the graph below. Label for the vertical axis of the graph below: 5 Click on the left button of your mouse to enter a corner point of your cobweb. You can always adjust the coordinates of the last point that you have entered using the field with dinates and pressing the return key. Label for the horizontal axis of the graph below: O Pt Oy O Pt+1 Ot Ox 6 = 16 (four iterations are enough). Remember to always start your cobweb on the horizontal f) Draw the cobweb diagram of the dynamical system with Po = 16 (four iterations are enough). Remember to always start your cobweb on the horizontal axis. Notice the axes may not start at zero in the graph below. Click on the left button of your mouse to enter a corner point of your cobweb. You can always adjust the coordinates of the last point that you have entered using the field with the coordinates and pressing the return key. Label for the horizontal axis of the graph below: Oy O Pt+1 Ot 0 x Opt Label for the vertical axis of the graph below: Ot Opt Ox Oy Pt+1 16- 14- 12- 10- 8 15 6 2. 9 10 Clear / Effacer 11 12 13 14 15 16 17 In a forest in Alberta, every year 85% of the population of red deer either die of natural causes or are eaten by predators. In the meantime, there are 8 new red deer per square kilometer. The discrete-time dynamical system (DTDS) that gives the population of red deer per square kilometer each year is Pt+1 = 0.15pt + 8 (Can you justify why it is the DTDS?) a) If there are 16 red deer per square kilometer now, how many red deer per square kilometer will there be in three years? Give your answer as a decimal with an accuracy of two decimal places. Answer: 9.43 b) Give the updating function f of the dynamical system, written as a function of a variable . f(x) = .15*x+8 Find its inverse, also written as a function of a variable x, if it exists. Write none if the inverse function doesn't exist. -(x) = c) Determine the equilibrium point p* of this dynamical system. Give exact values, not decimals; for instance, 2; 7; 7/3. d) Find the general solution of the dynamical system (ie., a formula in terms of t) given the initial condition po = 16. Use exact values, not decimals. Pt = e) Graph the points of the solution of the discrete time dynamical system with po = 16 (four values in addition to the initial condition are enough). Click on the left button of your mouse to enter point of your graph. You can always adjust the coordinates of the last point that you have entered using the field with the coordinates and pressing the return key. Label for the horizontal axis of the graph below: O Pt+1 O x Ot O pt Oy Label for the vertical axis of the graph below: O Pt+1 O Pt Oy Ot Ox Label for the vertical axis of the graph below: O Pt+1 pt Ot Ox -1 16- 14- 12- 10- 8 6 4 2 0 Clear Coordinates 1 2 3 4 f) Draw the cobweb diagram of the dynamical system with po axis. Notice the axes may not start at zero in the graph below. Label for the vertical axis of the graph below: 5 Click on the left button of your mouse to enter a corner point of your cobweb. You can always adjust the coordinates of the last point that you have entered using the field with dinates and pressing the return key. Label for the horizontal axis of the graph below: O Pt Oy O Pt+1 Ot Ox 6 = 16 (four iterations are enough). Remember to always start your cobweb on the horizontal f) Draw the cobweb diagram of the dynamical system with Po = 16 (four iterations are enough). Remember to always start your cobweb on the horizontal axis. Notice the axes may not start at zero in the graph below. Click on the left button of your mouse to enter a corner point of your cobweb. You can always adjust the coordinates of the last point that you have entered using the field with the coordinates and pressing the return key. Label for the horizontal axis of the graph below: Oy O Pt+1 Ot 0 x Opt Label for the vertical axis of the graph below: Ot Opt Ox Oy Pt+1 16- 14- 12- 10- 8 15 6 2. 9 10 Clear / Effacer 11 12 13 14 15 16 17
Expert Answer:
Related Book For
Differential Equations and Linear Algebra
ISBN: 978-0131860612
2nd edition
Authors: Jerry Farlow, James E. Hall, Jean Marie McDill, Beverly H. West
Posted Date:
Students also viewed these mathematics questions
-
Questions 8 & 9 For a Q system, the lead-time (LT) is 3 days. Inventory level and inventory position on day 1 are both 200 units. ROP is 250 and order quantity is 275. Withdrawals during next 10 days...
-
In a Hopfield neural network configured as an associative memory, with all of its weights trained and fixed, what three possible behaviours may occur over time in configuration space as the net...
-
QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...
-
Consider the points P(1, 2, k) and Q(2,-1, 1) and let u be the equivalent vector to the directed line segment PO. If us = 2, what is the value of k? A-1 OB. 1 OC2 D. 3 O EO
-
To what extent do you believe employers should accommodate employee expressions of their ethnic/cultural heritage with respect to their attire, work schedule, and similar activities? Employers are...
-
A British pharmaceutical chain wishes to make its first entry into the Canadian market by building a facility in southern Ontario, a region with which its director, Doug Moodie, is comfortable...
-
What is the purpose in using each of the following ratios: (a) current ratio (b) net profit after tax : revenue (c) asset turnover (d) interest cover (e) dividend cover?
-
An Ionic Crystal Figure shows eight point charges arranged at the corners of a cube with sides of length d. The values of the charges are +q and -q, as shown. This is a model of one cell of a cubic...
-
Question 10 (1 point) Find the center and radius of the circle with the given equation (2 + 2)+(y-6) = 36 (2, -6); 6 (-2, 6); 6 (-2, 6); 36 (2, -6); 36 Previous Page Next Page
-
If you are conducting a research proposal about how pet ownership benefits college students mentally and physically using a correlational design, what kind of methodology would you use? Specifically...
-
Case 13: Panera Bread Company in 2016Is the Companys Strategy to Rejuvenate Its Growth Working? by Arthur A. Thompson (page C-142)
-
What is the impact of the Florida Supreme Court's ruling that a real estate broker's relationship to the public "exacts the highest degree of trust and confi- dence" on sales associates? What is a...
-
3. [10 pts] Consider the following demand function d(x) and supply function s(x). d(x) = 700 -0.6x s(x) = 0.8x a) Find the market demand (equilibrium point the positive x value where demand and...
-
Given: f ( x ) = ( 2 x + 3 ) sin ( x ) , find the first derivative of this function.
-
Set in April 2016, this case invites students to assess FedEx Corp.'s and United Parcel Service, Inc.'s (UPS's) financial performance. The two firms have competed for dominance of the...
-
how to make bullet point example from this paragraph Ethical research Ethical research is a study that respects the rights of participants and yields accurate and reliable results. When it comes to...
-
At the beginning of its fiscal year, Lakeside Inc. leased office space to LTT Corporation under a seven-year operating lease agreement. The contract calls for quarterly rent payments of $25,000 each....
-
At 1:00 PM, Carlos puts into the refrigerator a can of soda, which has been standing out in a room with temperature 70F. The temperature inside the refrigerator is 40F. Fifteen minutes later, at 1:15...
-
Determine whether or not the mappings in Problems a to c are linear transformations from R to R (a and b are real constants). a. T (x) = x b. T (x) = ax + b c. T (x) = 1 / ax + b
-
Cauchy-Euler Systems The system where A is a constant matrix and t > 0.is called a system. (a) Show tht the Cauchy-Euler system has a solution of the form where is an eigenvalue of A and is a...
-
Explain the difference between total absorption costing and activity-based costing.
-
What are the key elements of ABC?
-
Discuss this statement. Revenue management does not always lead to profit maximisation so should not be used.
Study smarter with the SolutionInn App