If $f$ denotes the ratio of the number of nuclei decayed $(N_{d})$ to the number of nuclei at $t=0$ $(N_{0})$,then for a collection of radioactive nuclei,the rate of change of $f$ with respect to time is given as: [$\lambda$ is the radioactive decay constant]

• A
  $\lambda(1-e^{-\lambda t})$
• B
  $-\lambda e^{-\lambda t}$
• C
  $\lambda e^{-\lambda t}$
• D
  $-\lambda(1-e^{-\lambda t})$