Answer :
Answer:
[tex](B) \dfrac{dM}{dt} = kM[/tex]
Step-by-step explanation:
Given the mass M(a decreasing function) of a sample of a radioactive element at time t.
The rate of change of the sample’s mass [tex]\dfrac{dM}{dt}[/tex], is proportional to the mass, M of the sample.
This is written as:
[tex]\dfrac{dM}{dt} \propto M[/tex]
Introducing the decay constant k,
[tex]\dfrac{dM}{dt} = kM[/tex]
This is the equation which model the relationship between the mass of the sample and the rate of change of the sample’s mass.
The other options are therefore invalid.
[tex](A)\dfrac{dM}{dt} = kt (C)\dfrac{dM}{dt} = \dfrac{k}{t} (D)\dfrac{dM}{dt} = \dfrac{k}{M}[/tex]