Iodine-131 has a half-life of 8 days. How long would it take for the number of unstable nuclei in the sample to be reduced from 1,000 to 125?

After one-half life: 16 mg

After 2-half lives: 8 mg

After 3-half lives: 4 mg

After 4-half lives: 2 mg

After 5-half lives: 1 mg

(5 half-lives) x (8 days/half-life) = 40 days  

or doing it the mathematical way:  Let z be the number of days to be found:

1 mg = 32 mg x (1/2)^(z / 8 days)  

1/32 = (1/2)^(z / 8 days)  

log (1/32) = (z / 8 days) x log (1/2)  

z / 8 days = log (1/32) / log (1/2)

z = 8 days x log (1/32) / log (1/2) = 40 days

Explanation: