In a certain tropical forest, “litter” [dead vegetation like leaves and vines] forms on the ground at the rate of 10 grams per square centimeter per year. At the same time, however, the litter is decomposing at the rate of 80% per year. Let f(t) be the amount of litter [in grams per square centimeter] present at time t. Find a differential equation satisfied by f(t). Then, show that this mathematical model predicts that the amount of litter in the forest will eventually stabilize. What is this ‘equilibrium level’ of litter? (Show all steps)

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.