Concept explainers
Student Project: Logistic Equation with a Threshold Population An improvement to the logistic model includes a threshold population. The threshold population is defined to be the minimum population that is necessary for the species to survive. We use the variable T to represent the threshold population. A differential equation that incoqoraes both the threshold population T and carrying capacity K is
where r represents the growth rate. as before.
1. The threshold population is useful to biologists and can be utilized to determine whether a given species should be placed on the endangered list. A group of Australian researchers say they have determined the threshold population for any species to survive: 5000 adults. (Catherine Gabby. “A Magic Number,” Americon Scientist 98(1): 24. doi:l0.1511/2010.82.24. accessed April 9. 2015. http//www.anwricansoentist.org/iswes/pub/amagic-number). Therefore we use T = 5000 as the threshold population in this project. Suppose that the environmental carrying capacity In Montana for elk Is 25.000. Set up Equation 4.12 using the carrying capacity of 25,000 and threshold population of 5000. Assume an annual net growth rate of 18%.
Want to see the full answer?
Check out a sample textbook solutionChapter 4 Solutions
Calculus Volume 2
Additional Math Textbook Solutions
Calculus Volume 1
Introductory Statistics
Finite Mathematics & Its Applications (12th Edition)
Mathematics for Elementary Teachers with Activities (5th Edition)
Mathematics All Around (6th Edition)
Probability and Statistics for Engineers and Scientists
- Newtons Law of Cooling Newtons law of cooling states that the rate of change of temperature of an object is proportional to the difference in temperature between the object and the surrounding medium. Thus, if T is the temperature of the object after t hours and TM is the constant temperature of the surrounding medium, then dTdt=k(TTM) where k is a constant. Use this equation in Exercises 58-61. Show that the solution of this differential equation is T=Cekt+TM where C is a constant.arrow_forwardWhat is the carrying capacity for a population modeled by the logistic equation P(t)=250,0001+499e0.45t ? initial population for the model?arrow_forwardEastern Pacific Yellowfin Tuna Studies to fit a logistic model to the Eastern Pacific yellowfin tuna population have yielded N=1481+36e2.61t where t is measured in years and N is measured in thousands of tons of fish. a. What is the r value for the Eastern Pacific yellowfin tuna? b. What is the carrying capacity K for the Eastern Pacific yellowfin tuna? c. What is the optimum yield level? d. Use your calculator to graph N versus t. e. At what time was the population growing the most rapidly?arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage