A radioactive substance decays according to the formula

Question

Q(t) = Q0e−kt
where Q(t) denotes the amount of the substance present at time t (measured in years), Q0 denotes the amount of the substance present initially, and k (a positive constant) is the decay constant.
(a) Find the half-life of the substance in terms of k.
(b) Suppose a radioactive substance decays according to the formula
Q(t) = 36e−0.0001074t
How long will it take for the substance to decay to half the original amount? (Round your answer to the nearest whole number.)

Answer 1

(a) The half-life of the substance is given by t1/2 = ln(2)/k.

(b) The amount of the substance present at time t is given by Q(t) = 36e−0.0001074t. To find the time it takes for the substance to decay to half the original amount, we solve for t when Q(t) = 18. This gives us t = ln(2)/0.0001074 ≈ 6,400 years.