Exponential decay

Question

42 Gram sample of a substance that used to treat thyroid disorders has a k-value of .124 find the half life in days to the nearest tenth

 

Answer 1

If the units of k are days^-1, then 

 

k = 0.124 days^-1

 

and the amount present as a function of time obeys the equation

 

N(t) = N(0)e^-kt = N(0)e^-0.124t, t in days

 

To get half life, set

 

1/2 = e^-0.124t 

 

and solve for t:

 

t_1/2 = ln(1/2) / (-0.124) days = 5.5899 days, i.e. about 5.6 days