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Calculus: Early Transcendental Functions (MindTap Course List)
- 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_forwardAbsolute extrema on open and/or unbounded regions If possible, find the absolute maximum and minimum values of the following functions on the region R. ƒ(x, y) = x + 3y; R = {(x, y): |x| < 1, |y| < 2}arrow_forwardTriple integrals Use a change of variables to evaluate the following integral. ∫∫∫D yz dV; D is bounded by the planes x + 2y = 1, x + 2y = 2,x - z = 0, x - z = 2, 2y - z = 0, and 2y - z = 3.arrow_forward
- INTEGRAL Find the function y in terms of x, given that y = – 1 when x = 2, if dy/dx = 3 - 2x Choices: y = 3x - (2/3) x^2 - (2/3) y = 3x - (2/3) x^2 + (5/3) None of the choices y = 3x - (2/3) x^2 - (5/3)arrow_forwardTrue or False:- in the given question , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false The line y = (1 -3 √0.5)x divides the region under the curve f (x) = x(1 - x)on [0, 1] into two regions of equal area.arrow_forwardfunction: f (x, y) = (2h - y)(y - x^2) a) find all critical points of function b) find the one critical point which is within the cross-section, A (or possibly on the boundary of A) *attached*arrow_forward
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- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning