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Which sample A or B shown in figure has ...

Which sample `A` or `B` shown in figure has shorter mean-life ?

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form fig. , we find that at `t=0, ((dN)/(dt))_(A)=((dN)/(dt))_(B)`
Therefore, `(N_(0))_(A)=(N_(0))_(B)`
At any subsequent time, `((dN)/(dt))_(B)lt((dN)/(dt))_(A)`
`:. lambda_(B)N_(B) lt lambda_(A)N_(A)`
As `N_(B) lt N_(A)` (rate of decay of B is slower)
`:. lambda_(B) lt lambda_(A)`
Hence, `tau_(B) lt tau_(A)`, i.e., mean life time of B is shorter than that of A.
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