Half-life is modeled by the formula [tex]A(t)=A_0( \frac{1}{2})^{ \frac{T}{t_{ \frac{1}{2} }}[/tex]. Here, [tex]A_0[/tex] is the initial quantity, [tex]A(t)[/tex] is the amount remaining after a time [tex]t[/tex], and [tex]t_{ \frac{1}{2}[/tex] is the half-life of the decaying quantity. You can plug in 1.000 for [tex]A_0[/tex], 6.55 for [tex]t[/tex], and 5.22 for [tex]t_{ \frac{1}{2}[/tex]. We are solving for [tex]A(t)[/tex].
This gives [tex]A(t)=1.000( \frac{1}{2})^{ \frac{6.55}{5.22} = 419.05 \ mg[/tex]. Be mindful of significant figures if your instructor cares about that.
419.05 mg cobalt-60
