A Very Shiny Nose?
If we assume the starting time is midnight one day, and they have to set off at midnight the next day, how many bacteria will we have at 00:30? How many at 02:00? How many at 23:30?
Since there is a half-life of 10 minutes (which means that every 10 minutes half of the molecules of $X$ disappear), you can probably ignore most of the $X$ produced until near the end of the 24 hours.
You will need an estimate for the volume of Rudolph's nose. You might like to model it as a sphere. You might find this webpage helpful.
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