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)=A0e^(-0.0194t)

Where t is the time in years

Solution

Let half life = T.

Then by definition it is the time taken for half of substance to decay.

Hence we have   A₀e^-0.0194T = A₀/2

               or       e^-0.0194T = 1/2

               or       -0.0194T = -ln 2

              or        T = (ln 2)/0.0194 = 35.7292361113 years

This is the required half life.