Answer:
[tex]\boxed{\text{1.81 da}}[/tex]
Explanation:
1. Calculate the decay constant
The integrated rate law for radioactive decay is 1
[tex]\ln\dfrac{A_{0}}{A_{t}} = kt[/tex]
where
A₀ and A_t are the counts at t = 0 and t
k is the radioactive decay constant
[tex]\ln \dfrac{846}{269} = k \times 3.00\\\\\ln3.145 = 3.00k\\1.146 = 3.00k\\\\k =\dfrac{1.146}{3}\\\\k = \text{0.382 /da}\\[/tex]
2. Calculate the half-life
[tex]t_{\frac{1}{2}} = \dfrac{\ln2}{k} = \dfrac{\ln2}{0.382} = \text{1.81 da}[/tex]
The half-life for decay is [tex]\boxed{\textbf{1.81 da}}[/tex].
