Question

Find the​ half-life of a radioactive​ element, which decays according to the function ​A(t)=A0e−0.0372t​, where t is the time in years.

Answer 1

SOLUTION;

Half life decay function is

Where

A_{​​​​​​O} = initial amount

A_{​​​​​}(t)= remaining amount after t time

For , half life

So, A_{​​​​​​o} = P ( supposed)

Then. A​​​​​(t)= P/2

Now,

P 2 Pe-0.0372

$\frac{1}{2} =e^{-0.0372t}$

$ln\frac{1}{2} =ln(e)^{-0.0372t}$

$ln\frac{1}{2} =-0.0372t$

The half life is = 18.6 years

Answer

18.6 years