So we want to know how long will it take cobalt 56 to decay to 62% to it's original value if we know that one half life is T₁/₂=79 days and it's decay constant is k=8.77*10^-3. The law for radioactive decay is:
N(t)=N₀e^-k*t, where N(t) is the quantity of the material in some time t, N₀ is the original quantity of the material, k is the decay constant, t is time.
N(t)=0.62*N₀ or 62% of the original value. 0.62*N₀=N₀e^-k*t, N₀ cancel out and we get:
0.62=e^-k*t
We need to get the time t. We get t if we take the natural logarithm of both sides:
ln(0.62)=-k*t*ln(e), ln(e)=1 so we have:
ln(0.62)=-k*t
t={ln(0.62)/(-k)} = 54.5.
Time for cobalt 56 to decay to 62% of its original value is 54.5 days.
![\begin{tabular} {|c|c|} Statement&Reason\\[1ex] Line m is parallel to line n&Given\\ \angle1\cong\angle2&Corresponding angles\\ m\angle1=m\angle2&Deifinition of Congruent angles\\ \angle2\ and\ \angle3\ form\ a\ linear\ pair&Adjacent angles on a straight line\\ \angle2\ is\ supplementary\ to\ \angle3&Deifinition of linear pair\\ m\angle2+m\angle3=180^o&Deifinition of supplementary \angle s\\ m\angle1+m\angle3=180^o&Substitution Property \end{tabular}](https://tex.z-dn.net/?f=%5Cbegin%7Btabular%7D%0A%7B%7Cc%7Cc%7C%7D%0AStatement%26Reason%5C%5C%5B1ex%5D%0ALine%20m%20is%20parallel%20to%20line%20n%26Given%5C%5C%0A%5Cangle1%5Ccong%5Cangle2%26Corresponding%20angles%5C%5C%0Am%5Cangle1%3Dm%5Cangle2%26Deifinition%20of%20Congruent%20angles%5C%5C%0A%5Cangle2%5C%20and%5C%20%5Cangle3%5C%20form%5C%20a%5C%20linear%5C%20pair%26Adjacent%20angles%20on%20a%20straight%20line%5C%5C%0A%5Cangle2%5C%20is%5C%20supplementary%5C%20to%5C%20%5Cangle3%26Deifinition%20of%20linear%20pair%5C%5C%0Am%5Cangle2%2Bm%5Cangle3%3D180%5Eo%26Deifinition%20of%20supplementary%20%5Cangle%20s%5C%5C%0Am%5Cangle1%2Bm%5Cangle3%3D180%5Eo%26Substitution%20Property%0A%5Cend%7Btabular%7D)
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