The radiation R(t) in a substance decreases at a rate that is proportional to the amount present; that is, dR = kR, where k is the constant of proportionality and t is the time measured dt in years. The initial amount of radiation is 7600 rads. After three years, the radiation has declined to 500 rads. (Note: One rad = 0.01– is a unit used to measure absorbed radiation kg doses). A) Express R as a function of time. B) When will the radiation drop below 20 rads? C) Find the half-life of this substance.

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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.