The half-life of krypton-85 is 11 days. How long will it take for 6.3% of a given amount of krypton-85 to be left?

Question

 this question involves solving with logarithms and exponentials

Answer 1

A(t) = amount remaining after t days

 

         = A₀e^kt, where A₀ is the initial amount

 

Since the half-life is 11 days, (1/2)A₀ = A₀e^11k

 

                                                            0.5 = e^11k

 

                                                             11k = ln0.5

 

                                                                 k = -0.063

 

A(t) = A₀e^-0.063t

 

Find t so that A(t) = 0.063A₀:   0.063A₀ = A₀e^_-0.063t

 

                                                      0.063 = e^-0.063t

 

                                                      ln(0.063) = -0.063t

 

                                                       t = 43.88 days