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## 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 t

Question

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

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Mathematics
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2021-08-26T05:23:04+00:00
2021-08-26T05:23:04+00:00 1 Answers
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## Answers ( )

Answer:2. dM/dt = -0.11M

Step-by-step explanation:Differential equations for proportional amouts:A differential equation for proportional amounts is given by:

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.