Radium 226 is used in cancer radiotherapy. Let P(t) be the number of grams of radium 226 in a sample remaining after t years, and let P(t) satisfy the differential equation P′(t) = -.00043P(t), P(0) = 12.

(a) Find the formula for P(t).

(b) What was the initial amount?

(c) What is the decay constant?

(d) Approximately how much of the radium will remain after 943 years?

(e) How fast is the sample disintegrating when just 1 gram remains? Use the differential equation.

(f) What is the weight of the sample when it is disintegrating at the rate of .004 gram per year?

(g) The radioactive material has a half-life of about 1612 years. How much will remain after 1612 years? 3224 years? 4836 years?