The substance's half-life is 6.77 days
N = [tex] N_{0} e^{-kT} [/tex]
Where,
[tex] N_{0} [/tex] = initial mass (at time t = 0)
N = mass at time t
k = a positive constant that depends on the substance itself and on the units used to measure time
t = time, in days
The, half life t[tex] T_{ \frac{1}{2}} [/tex] = ?
Then at half life, the sample will remain half., i.e.
N ([tex] T_{ \frac{1}{2}} [/tex]) = [tex] \frac{N}{2} [/tex]
⇒ [tex] \frac{39}{2} [/tex] = 39 [tex] e^{- 0.1024 t} [/tex]
⇒ ln 0.5 = -0.1024t
⇒ t = 6.77 days
