An activity of is needed in a radioactive sample to be used in a medical procedure. One week before the treatment, a nuclide sample with a half-life of is prepared. We have to find the activity of the sample at the time of preparation in order that it has the required activity at the time of treatment.

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A nuclide sample with a half-life of is to be prepared so that a week later it has an activity of .

The disintegration constant of the nuclide will be

We note that

We recall that variation of decay rate with time is given by the relation

We require

Therefore,