(a) The population p(t) of Loompaland (home to the Oompa Loompas) in 1920 and 1970 was...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
(a) The population p(t) of Loompaland (home to the Oompa Loompas) in 1920 and 1970 was 530 and 2310, respectively. Predict its population in 2020 and 2070 using the exponential model for population growth dp = kp. dt (1) (b) The population of Loompaland in 2020 is actually 7600 Oompa Loompas. i. Correct your prediction for the the population of Ooompa Loompas in 2070 using the logistic model of population growth dr = rp(1-). (Help: The relative growth rate r for the logistic model (2) is r = 0.031476.) ii. What is the carrying capacity N of Loompaland? iii. In what year will the population reach 99% of N? (c) The infamous chocolatier Willy Wonka reopens his chocolate factory and starts hiring Ooompa Loompas, who emigrate from Loompaland at a rate proportional to the population p. i. Modify the logistic ODE (2) to include emigration at a rate proportional to the population p. ii. Non-dimensionalise your model in (c)i. by introducing non-dimensional pa- rameters: T = rt. N' iii. Using the linear stability criteria and phase lines, analyse your non-dimensional emigration model for all possible scenarios. iv. What do your results tell you about the future population of Loompaland? (a) The population p(t) of Loompaland (home to the Oompa Loompas) in 1920 and 1970 was 530 and 2310, respectively. Predict its population in 2020 and 2070 using the exponential model for population growth dp = kp. dt (1) (b) The population of Loompaland in 2020 is actually 7600 Oompa Loompas. i. Correct your prediction for the the population of Ooompa Loompas in 2070 using the logistic model of population growth dr = rp(1-). (Help: The relative growth rate r for the logistic model (2) is r = 0.031476.) ii. What is the carrying capacity N of Loompaland? iii. In what year will the population reach 99% of N? (c) The infamous chocolatier Willy Wonka reopens his chocolate factory and starts hiring Ooompa Loompas, who emigrate from Loompaland at a rate proportional to the population p. i. Modify the logistic ODE (2) to include emigration at a rate proportional to the population p. ii. Non-dimensionalise your model in (c)i. by introducing non-dimensional pa- rameters: T = rt. N' iii. Using the linear stability criteria and phase lines, analyse your non-dimensional emigration model for all possible scenarios. iv. What do your results tell you about the future population of Loompaland?
Expert Answer:
Related Book For
Posted Date:
Students also viewed these mathematics questions
-
A population is growing at a rate proportional to its size. After 5 years, the population size was 164000. After 12 years, the population size was 235000. What was the original population size?
-
A bacterial population grows at a rate proportional to its size. Initially, it is 10000, and after 10days it is 20000. What is the population after 25 days?
-
A radioactive element decays at a rate proportional to the amount present. Suppose an initial mass of 10 grams decays to 8 grams in 3 hours. Find the half-life of the element-the time taken to decay...
-
1. What is the present value (PV") of an offer of $15,000 two years from now if the Opportunity Cost of Capital (OCC) is $12% per annum? 2. What is the PV of an offer to receive $12,000 three years...
-
Compound Y (C8H4O3) dissolves slowly when warmed with aqueous sodium bicarbonate. The IR spectrum of Y has strong peaks at 1779 and at 1854 cm-1. The broadband proton-decoupled 13C spectrum of Y...
-
The manufacturing costs of Ackerman Industries for the first three months of the year follow: Total Costs Units Produced January.$1,900,00020,000 units February.2,250,000.27,000...
-
Describe the common models of managed care organizations.
-
Sommer Graphics Company was organized on January 1, 2019, by Krystal Sommer. At the end of the first 6 months of operations, the trial balance contained the accounts shown below. Analysis reveals the...
-
21) A machinist turns on the power on to a grinding wheel at time t=0s. The wheel accelerates uniformly from rest for 10 s and reaches the operating angular speed of 58 rad/s. The wheel is run at...
-
Richardson Ski Racing (RSR) sells equipment needed for downhill ski racing. One of RSRs products is fencing used on downhill courses. The fence product comes in 150-foot rolls and sells for $215 per...
-
In microscopy why is it important for a microscope to reach the focal plane when observing a microscopic organism? Does the field of view increase or decrease when you go from a low power objective...
-
Can you elaborate on the applications of CRISPR-Cas9 technology beyond genome editing, such as epigenome modulation, gene regulation, and base editing ?
-
According Zittrain, what are the five principal factors that contribute to generativity?
-
Explain what aspects of organized anarchy make higher education more adaptable and less adaptable and support with research ?
-
On January 1, 2023, Wheeler Inc (a calendar year end business) purchases a building for $2,000,000 and places it into service. When Wheeler Inc records depreciation on the building on December 31,...
-
Are you an adaptable or resilient person? What do you think are the qualities a person should have to be adaptable and resilient?
-
Please go to Yahoo Finance and search out any company's stock information. Under "Option" tab, look up the list of prices for different strike prices for calls and puts that are expiring on Dec 2022...
-
Consider the following cash flows in Table P5.5. (a) Calculate the payback period for each project. (b) Determine whether it is meaningful to calculate a payback period for project D. (c) Assuming...
-
Use Algorithm 4.4 with n = m = 4 to approximate the following double integrals, and compare the results to the exact answers. 2.5 14 ay dy dx J2.1 12 0.5 0.5 (2 y) dy dx
-
The study of mathematical models for predicting the population dynamics of competing species has its origin in independent works published in the early part of the 20th century by A. J. Lotka and V....
-
Find the first three iterations obtained by the Power method applied to the following matrices. a. Use x(0) = (1, 2, 1)t. b. Use x(0) = (1, 1, 0, 1)t. c. Use x(0) = (1, 1, 0,3)t. d. Use x(0) = (0, 0,...
-
The codon change (Gly-12 to Val-12) in human H-ras that converts it to oncogenic H-ras has been associated with many types of cancers. For this reason, researchers would like to develop drugs to...
-
Outline the general strategy used in metagenomics.
-
You need to understand the approach described in question 3 in More Genetic TIPS before answering this question. A muscle-specific gene was cloned and then subjected to promoter bashing. As shown...
Study smarter with the SolutionInn App