A radio 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 : a/2=ae^−3.568t

Question

A radio 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 : a/2=ae^−3.568t

sillybilly123 · Answer

$\dfrac{a}{2}=a e^{ - 3.568 ~ T}$

$\implies \frac{1}{2}=e^{ - 3.568 ~ T}$

$ \implies \ln ( \frac{1}{2} )= \ln e^{ - 3.568t ~ T }$

$\implies \ln (1) - \ln (2) = - 3.568 ~ T$

finish that off  :)

NB, using *T* rather than *t*, as this is a specific instance of the decay equation.  ie the $\dfrac{a}{2}=a e^{ - 3.568 ~ t}$ is only true for t = the half-life = T.