(a)
To calculate: The marginal utility of product x if the utility function
(b)
To calculate: The marginal utility of product y if the utility function
(c)
Whether a person should consume one more unit of product of x or one unit of product of y if
(d)
To graph: The function
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Calculus: An Applied Approach (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_forwardFind the constant of proportionality. z is directly proportional to the sum of x and y. If x=2 and y=5, then z=28.arrow_forward
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