The rate at which a quantity M of a certain radioactive substance decays is proportional to the amount of the substance present at a given time. Which of the following is a differential equation that could describe this relationship?
1. dM/dt = -3.72 t^2
2. dM/dt = -0.11M
3. dM/dt = 0.08 t^2
4. dM/dt = 1.2M
Question
Answer:
2. dM/dt = -0.11M
Step-by-step explanation:
Differential equations for proportional amouts:
A differential equation for proportional amounts is given by:
[tex]\frac{dx}{dt} = ax[/tex]
In which a is the constant rate. If the amount increases, a is positive. If it decays, b is positive.
In this question:
Decays, so a < 0.
Proportional to the amount of the substance present at a given time, which means that a multiplies the amount M.
This means that the correct answer is given by option 2.