The decay equation is of the form
[tex]m(t) = m_{0} e^{-kt}[/tex]
where
m(t) = the mass remaining after t minutes
m₀ = the initial mass
k = constant
Because the half-life is 3 minutes, therefore
[tex]e^{-3k} = \frac{1}{2} [/tex]
Therefore
-3k = ln(0.5)
k = ln(0.5)/(-3) = 0.231
Because m₀ = 16 mg, the time, t, for the mass to decay to 1.0 mg is given by
[tex]e^{-0.231t} = \frac{0.1}{16} =0.00625 \\\\
-0.231t = ln(0.00625) \\\\ t = \frac{ln(0.00625)}{-0.231} =21.97 \, min[/tex]
Answer: 22 min (nearest integer)
