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...

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 = R − A, 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 e−k . Find a formula for D in terms of R and k. Reminder: ab

c. Explain why A = R − Re−kt .