Explanation

(d) Activity $A = \lambda\ N_{0}e^{- \lambda t}$
$\Rightarrow \log_{e}A = \log_{e}\lambda N_{0} + \log_{e}e^{- \lambda t}$
$\Rightarrow \log_{e}A = \log_{e}C - \lambda t$ [Take $\lambda N_{0} = C$]
$\Rightarrow \log_{e}A = - \lambda t + \log_{e}C$
This is the equation of a straight line having negative slope $( = - \lambda)$ and positive intercept on $\log_{e}A$ axis