Question

A radio active isotope decays according to the exponential decay equation where t is in days. Round to the thousandths place. The half life is the solution (t) of the equation: a/2=ae^-2.360t

Answer 1

to calculate the value of the half life we proceed as follows;
a/2=ae^(-2.360t)
the a(s) will cancel and we shall remain with:
1/2=e^-2.360t
introducing the natural logs we get:
ln (1/2)=ln e^(-2.360t)
ln(1/2)=-2.360t
hence;
t=(ln 0.5)/(-2.360)
t=0.294
the answer is t=0.294