Help Please! Confused on a problem!

Question

A radioactive substance has a half-life of 20 years. If 3631 lbs. are stored, 

A) How much will be present in 15 years?    Blank 1. Calculate the answer by read surrounding text. lbs

B) How much will there be after 35 years? (Can you do this without calculations based on part A?)   Blank 2. Calculate the answer by read surrounding text. lbs

C) When will there be about 218 lbs.?   Blank 3. Calculate the answer by read surrounding text. years

Answer 1

half life of 20 years

1/2 = e^rt = e^20r

ln.5 = 20r

r = ln.5/20 = -0.03466 = about 3.5% rate of decay

P = Ae^-.03466t

P(15) = 3631e^-.03466(15) = 3631(.5946) = 2159

P(35) = 3631e^-.03466(15) = 1079.4

P(40) is 2 half lives or 1/4 of 3631 = 908. P(35) > 908

P(20) = 3631e^-.03466(20) = 1815.5 = half of 3631

P(15) is greater than P(20). 2159>1816

218 = 3631e^-0.03466t

218/3631 = e^-0.03466t

-.03466t = ln..06

t = ln.06/-.03466 = 81.15 years to reach 218

80 is 4 half lives or 1/2^4 = 1/16 x 3631 = 227

it decays a little more in 81 years to 218