Find the halflife of a radioactive element which decays acco

Find the half-life of a radioactive element, which decays according to the function A(t) = A_0e^-0.0182t, where t is the time in years.

The half-life of the element is __ years.

(Round to the neareth tenth)

Solution

For

A = Ao exp (-kt)

The half life is given by

half life = ln(2) / k

Thus, as k = 0.0182 here,

half life = ln(2) / 0.0182 = 38.08500992 = 38.1 years [ANSWER]