The activity of a certain radioactive sample is plotted against time in graph. If the initial slope of the curve is m, then find the slope of the curve at point P ?

Explanation

Activity `A=A_0 e^(-lambdat)`
Slope of the graph is `(dA)/(dt)=-lambdaA_0e^(-lambdat)`
Initially `t=0 rArr (dA)/(dt)=-lambdaA_0` (=m) given
Slope of point P is , `(dA)/(dt)=-lambdaA_0 e^(-lambdatau)`
`=m/3 [ because lambdatau=1]`