If $\mathrm{T}$ is the half-life of a radioactive substance then its instantaneous rate of change of activity is proportional to

• A

  $\sqrt{\mathrm{T}}$
• B

  $\mathrm{T}$
• C

  $\mathrm{T}^{2}$
• Correct answer
  D

  $\mathrm{~T}^{-2}$

Hence, the correct answer is option: 'D'.