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 the sample 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?