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A radiocative substance for a medical treatment needs to prepared in a laboratory, transported to the hospital and administered to a partient. Suppose $150mg$ of the substance is required for the treatment and it takes $45$ minutes to travel from the laboratory to the hospital. If the half$-$life of the substance is $4$ hours, how much of the radioactive substance in mg must the laboratory prepare so enough remains for the treatment after transportation?

Enter your answer below round to two decimal places.

Hint: Keep to one single time unit.

$mg$