A 50.0g g sample of 16n decays to 12.5g in 14.4 seconds. What is its half life

T is amount after time t

Ao is initial amount

t is time

HL is half life

log (At) = log [ Ao x (1/2) ^ (t/HL) ]

log (At) = log Ao + log (1/2) ^ (t/HL)

log (At) = log Ao + (t/HL) x log (1/2)

(log At - log Ao) / log (1/2) = t / HL

log (At/Ao) / log (1/2) = t / HL

HL = t / [ (log (At / Ao)) / log (1/2) ]

HL = 14.4 s / [ (log (12.5 / 50) / log (1/2) ]

HL = 14.4 s / 2 = 7.2 seconds