Sodium-24 has a half-life of 14.8 hours. how much of a 227.0 mg sodium-24 sample will remain after 3.7 days?

For this problem we can use half-life formula and radioactive decay formula.

Half-life formula,
t1/2 = ln 2 / λ

where, t1/2 is half-life and λ is radioactive decay constant
t1/2 = 14.8 hours

Hence,
          14.8 hr    = ln 2 / λ
                    λ   = ln 2 / 14.8 hr 

Radioactive decay law,
Nt = No e∧(-λt)

where, Nt is amount of compound at t time, No is amount of compound at      t = 0 time, t is time taken to decay and λ is radioactive decay constant.

Nt = ?
No = 227.0 mg
λ   = ln 2 / 14.8 hr = 0.693 / 14.8 hr
t    = 3.7 days = 3.7 x 24 hours

By substituting,
Nt = 227 mg e∧((-0.693/14.8)x3.7 x24))
Nt = 3.5 mg

Hence, mass of remaining sample after 3.7 days = 3.5 mg