A sample of 8 grams of radioactive material is placed in a vault. Let P(t) be the amount remaining after t years, and let P(t) satisfy the differential equation P(t) = -.021P(t). (a) Find the formula for P(t) (b) What is P(0)? (c) What is the decay constant? (d) How much of the material will remain after 10 years? (e) Use the differential equation to determine how fast thesample is disintegrating when just 1 gram remains. (f) What amount of radioactive material remains when it is disintegrating at the rate of .105 gram per year? (g) The radioactive material has a half-life of 33 years. How much will remain after 33 years? 66 years? 99 years?

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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.