Aradio active isotope decays according to the exponential decay equation where t is in days. round to the thousandths place. for the half life: the half life is the solution (t) of the equation : a2=ae−7.571t a 2 = a e − 7.571 t

The decay function is

where
a₀ = initial mass
t = time, days

At half life, a(t) = a₀/2, therefore the time required to achieve half life is given by the equation


Take natural log of each side.
ln(1/2) = -7.571 t

Divide each side by -7.571 to obtain


0.0192 days (nearest thousandth)