Answer
2.4 mg
Work Step by Step
The amount of radionuclide at the beginning is $A_{0}=9.6\,mg$
Rate constant $k=\frac{0.693}{t_{1/2}}=\frac{0.693}{14.3\,day}=0.04846/day$
Time $t=28.6\,days$
$\ln(\frac{A_{0}}{A})=kt$ where $A$ is the amount of radionuclide remaining.
$\implies \ln(\frac{9.6\,mg}{A})=0.04846\times28.6=1.386$
Taking the inverse $\ln$ of both sides, we have
$\frac{9.6\,mg}{A}=e^{1.386}=3.9988$
Or $A= \frac{9.6\,mg}{3.9988}=2.4\,mg $
