Given:
The rate of decay,
[tex]\frac{dM}{dt}=-kM[/tex]
The initial mass, M=150 g
To find:
The expression for the mass at any time t.
Explanation:
On rearranging the given equation,
[tex]\frac{dM}{M}=-\text{kdt}[/tex]
On integrating the above equation,
[tex]\begin{gathered} \text{lnM=-kt} \\ \Rightarrow M=e^{-kt} \end{gathered}[/tex]
Final answer:
Thus the expression for the mass at any time t is
[tex]M=e^{-kt}[/tex]
Therefore the correct answer is option A.
