The mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of 8.1% per day. find the half-life of this substance (that is, the time it takes for one-half the original amount in a given sample of this substance to decay).

The general equation for radioactive decay is;

N = N₀e^ (-λt)

x - decay constant (λ) - rate of decay

t - time

N - amount remaining after t days, since we are calculating the half life, amount of time it takes for the substance to to be half its original value, its N₀/2

N₀ - amount initially present

substituting the values

N₀/2 = N₀e^ (-0.081t)

0.5 = e^ (-0.081t)

ln (0.5) = - 0.081t

-0.693 = - 0.081t

t = 0.693 / 0.081

= 8.55

half life of substance is 8.55 days