Question 836622
The half life is the amount of time for half of the substance to disintegrate.


Since the sample decays exponentially, the amount A(t) of the substance as a function of time t (in hours) is given by


*[tex \Large A(t) = A_0 e^{-kt}]


where k is a positive constant. The half-life is 2 hours. Assume A_0 = 1. Then


*[tex \Large 0.5 = e^{-2k} \Rightarrow -2k = \ln 0.5 \Rightarrow k = -\frac{\ln 0.5}{2} \approx. 0.3465]


Substitute this value of k, as well as t = 1, t = 7, to find the answers to (a) and (b).