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Question
Express the following physical statements in the form of differential equation.
Radium decays at a rate proportional to the amount Q present
Solution
If at anytime t
The amount of Radium present is Q.
The rate at which Q is decreasing is `"dQ"/"dt"` and this is negative.
This rate of decrease or decay is found to be proportional to Q itself.
Hence we have the law, `"dQ"/"dt"` = – KQ
Where k is a positive constant.
Therefore `"dQ"/"dt" +"kQ"` = 0
Which is a differential equation.
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