An unknown radioactive element decays into non-radioactive substances. In 960 days the radioactivity of a sample decreases by 42 percent.

Question

 What is the half-life of the element?

How long will it take for a sample of 100 mg to decay to 46 mg?

Answer 1

y=ae^rt

a)

1-0.42 = 0.58

y/a = 0.58=e^960r

r=ln(0.58)/960

y = a(0.58)^t/960

y/a = 0.5 = (0.58)^t/960

t/960 = ln(.5)/ln(.58)

t = 960(1.272) ≈ 1222 days

b)

46 = 100(0.58)^t/960

t= 960ln(0.46)/ln(0.58) = 1368.5 days