determine how much of a drug is absorbed into the body, researchers measure the difference between the dosage D and the amount of the drug excreted from the body. The total amount excreted is found by integrating the excretion rate r(t) from 0 to ∞. Therefore, the amount of the drug absorbed by the body is D −  ∞   0 r(t) dt. If the initial dose is D = 150 milligrams (mg), and the excretion rate is r(t) = 50e−0.5t mg per hour, find the amount of the drug absorbed by the body.

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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.