Holling’s Functional Response Curve The total number P of prey taken by a predator depends on the availability of prey. C.S. Holling proposed a function of the form
Where P is the number of cocoons parasitized and n is the density of cocoons available (measured as number per square inch).
a) Draw a graph of p versus n. Include values of n up to 2 cocoons per square inch.
b) What density of cocoons will ensure that the wasp will find and parasitize 6 of them?
c) There is a limit to the number of cocoons that the wasp is able to parasitize no matter how readily available the prey may be. What is this upper limit?
Trending nowThis is a popular solution!
Chapter 2 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Additional Math Textbook Solutions
College Algebra (5th Edition)
Intermediate Algebra (7th Edition)
College Algebra (7th Edition)
Intermediate Algebra (13th Edition)
Elementary & Intermediate Algebra
Elementary and Intermediate Algebra: Concepts and Applications (7th Edition)
- Decay of Litter Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be the amount of litter present, in grams per square meter, as a function of time t in years. If the litter falls at a constant rate of L grams per square meter per year, and if it decays at a constant proportional rate of k per year, then the limiting value of A is R=L/k. For this exercise and the next, we suppose that at time t=0, the forest floor is clear of litter. a. If D is the difference between the limiting value and A, so that D=RA, then D is an exponential function of time. Find the initial value of D in terms of R. b. The yearly decay factor for D is ek. Find a formula for D in term of R and k. Reminder:(ab)c=abc. c. Explain why A=RRekt.arrow_forwardHydroplaning On wet roads, under certain conditions the front tires of a car will hydroplane, or run along the surface of the water. The critical speed V at which hydroplaning occurs is a function of p, the tire inflation pressure. The following table shows hypothetical data for p, in pounds per square inch, and V, in miles per hour. Tire inflation pressure p Critical speed V for hydroplaning 20 46.3 25 51.8 30 56.7 35 61.2 a Find a formula that models V as a power function of p. b In the rain, a car with tires inflated to 35pound per square inch is travelling behind a bus with tires inflated to 60 pounds per square inch, and both are moving at 65 miles per hour. If they both hit their brakes, what might happen?arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage