Weekly Challenge 48: Quorum-sensing

Age 14 to 16 Short Challenge Level:

    Rudolph's nose glows because it is home to a species of bacteria, Vibrio rudolphi, that luminesces when it reaches a certain population density. It detects the size of its population by quorum sensing: each bacterial cell releases a signal molecule, X, at a rate of $1$ per minute and if the concentration of X is greater than or equal to $10^{11}$ cells/ml, the bacteria will glow. X decays with a half life of ten minutes but the bacteria divide every 30 minutes.

    Sadly, Rudolph catches a nasty cold, which, by the time he is better, has killed all of the bacterial cells in his nose except for one. Santa is worried: there are only 24 hours left until Christmas. Will Rudolph's nose be glowing again in time?

    If you need any data that is not included, try to estimate it: Santa wants an answer now, so that he can make alternative plans if need be.
    Did you know ... ?

    The mathematics of rates and half-lives are of great importance in mathematical biology where growth factors are often in competition with decay factors.

    You can find more short problems, arranged by curriculum topic, in our short problems collection.