The decay function is of the form
[tex]N(t) = N_{0} \, e^{-kt}[/tex]
where
N₀ = initial amount
k = decay constant
t = hours
The material decays by 10% in 95 hours. Therefore
[tex]0.9N_{0} = N_{0} \, e^{-95k} \\\\ -95k = ln(0.9) \\\\ k= \frac{ln(0.9)}{-95}=0.001109[/tex]
The time for the half life is given by
[tex]0.5N_{0} = N_{0} \, e^{-0.001109t} \\\\ -0.0001109t = ln(0.5) \\\\ t = \frac{ln(0.5)}{-0.001109} = 625 \, h[/tex]
Answer: The half life is 625 hours
