Marginal revenue, cost, and profit, Let
Find each of the following
a.
b.
c.
d.
e. Describe what each quantity in parts (b) and (d) represents
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
Calculus and Its Applications (11th Edition)
Additional Math Textbook Solutions
Calculus: Early Transcendentals (3rd Edition)
University Calculus: Early Transcendentals (4th Edition)
Calculus & Its Applications (14th Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
- 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_forwardWater Flea F. E Smith has reported on population growth of the water flea. In one experiment, he found that the time t, in days, required to reach a population of N is given by the relation e0.44t=NN0(228N0228N)4.46. Here N0 is the initial population size. If the initial population size is 50, how long is required for the population to grow to 125?arrow_forwardHollings 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 P=cn(1+dn) to model the number of prey taken in certain situations. Here n is the density of prey available, and c and d are constants that depend on the organisms involved as well as on other environmental features. Holling took data gathered earlier by T. Burnett on the number of sawfly cocoons found by a small wasp parasite at given host density. In one such experiment conducted, Holling found the relationship p=21.96n1+2.41n, 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?arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage