Question

Half-Life N(t)=No(12)th N= final amount No= initial amount t= time h= half-life Iodine-123 is sometimes used in thyroid scans and has a half-life of 15 hours. a) How much of a 250 mg sample would remain after 40 hours (round to hundredths)? b) How much time does it take for 250 mg to decay to 100 mg (round to the nearest hour)? Use logarithms to solve it algebraically. You must show your work for each step to get credit.

Answer 1

a)39.37 mg

b) 20 hours

Explanation:

Half-Life N(t)=No(12)th N= final amount No= initial amount t= time h= half-life Iodine-123 is sometimes used in thyroid scans and has a half-life of 15 hours.

a) How much of a 250 mg sample would remain after 40 hours (round to hundredths)?

We are to find N(t)

N(t) = No (1/2)^t/t½

No = 250mg

t = 40 hours

t½ = 15 hours

N(t) = 250 (1/2)^40/15

N(t) = 39.372532809215 mg

Approximately = 39.37 mg

b) How much time does it take for 250 mg to decay to 100 mg (round to the nearest hour)? Use logarithms to solve it algebraically.

We are to find time t

t = t½ (In Nt/No)/- In 2

t = 15 × (In 100/250)/ -In2

t = 19.82892142331 hours

Approximately = 20 hours