Ten grams of a radioactive substance with decay constant .04 is stored in a vault. Assume that time is measured in days, and let P(t) be the amount remaining at time t. (a) Give the formula for P(t) (b) Give the differential equation satisfied by P(t). (c) How much will remain after 5 days? (d) What is the half-life of this radioactive substance?

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A:

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.