How do you determine the total mass of an original 28.0-milligram sample of Po-210 that remains unchanged after 414 days?

Given the 138.4 day half-life of the radioisotope $3.5 \cdot m g$ of ""^210Po will remain.
Given the boundary conditions of the problem it was SPECIFIED that the mass of ""^210Po remained unchanged. I acknowledge, however, that this is a radioactive decay problem, and ""^210Po is a screaming hot isotope and $\alpha - \text{emitter}$ with a half-life of 138.4 days; these data SHOULD have been supplied with the problem.
And so your polonium isotope has experienced 3 half-lives.........And there is thus ${\left(\frac{1}{2}\right)}^{3} = \frac{1}{8}$ of the original mass, i.e. $3.5 \cdot m g$.