Strontium 60 is a radioactive material that decays according

Strontium 60 is a radioactive material that decays according to the function: A(t)=A₀e^-0.03664t, where A₀ is the initial amount present and A is the amount present after t years. Assume that a scientist has a sample of 300 grams of strontium 60.

a) What amount will be present in 10 years?

b) What is the half life of strontium 60?

Solution

A = A_oe^-0.03664t

initial amount A_o = 300 grams

a) t = 10 years

==> A = 300 e^-0.03664(10) = 300 e^-0.3664

==> A = 300 (0.69326)

==> A = 207.978

Hence 207. 978 grams will be left after 10 years

b) half life ==> Amount present after t years becomes half of initial amount

==> A(t) = A_o/2

==> A_o/2 = A_o e^-0.03664t

==> 1/2 = e^-0.03664t

apply natural logarithms on both sides

==> ln (1/2) = ln e^-0.03664t

==> -ln2 = -0.03664t lne

==> t = (ln 2)/(0.03664)

==> t = 18.9178 approximately 19

Hence half life of strontium 60 is 19 years