PoSWW 11: Pinpoint Inaccuracy

This one comes courtesy of Christian, an occasional commenter and professional nitpicker (for which we are very grateful). It is a question from a 2016 Abitur (final year) exam for the German state of Hesse. (We know little of how the Abitur system works, and how this question may fit in. In particular, it is not clear whether the question above is a statewide exam question, or whether it is more localised.)

Christian has translated the question as follows:

A specialty store conducts an ad campaign for a particular smartphone. The daily sales numbers are approximately described by the function g with \color{blue}\boldsymbol{g(t) = 30\cdot t\cdot e^{-0.1t}}, where t denotes the time in days counted from the beginning of the campaign, and g(t) is the number of sold smartphones per day. Compute the point in time when the most smartphones (per day) are sold, and determine the approximate number of sold devices on that day.

11 Replies to “PoSWW 11: Pinpoint Inaccuracy”

    1. Yes, it may be the translation makes it sound worse than it is. Though I can’t think of any way the question could be reasonable.

    2. I chose “point in time” as translation because it is the literal equivalent of the German “Zeitpunkt”; because a trustworthy online source gave it; and because I wanted to preserve in the translation that a single time-point (heh, heh) and not a time interval was referred to in this context. Translation is not professional, Marty kindly provided the original for those who may want to do better than I did.

      1. Thanks, Christian. There are always nuances with translations, and examiners can be cute with wording, skating incorrectness without quite falling in. But it’s difficult to imagine that the solid meaning of “Zeitpunkt” is anything other than your translation indicates.

      2. Fair enough. I have no doubt VCAA has used the phrase “point in time” on at least one occasion.

        I don’t like the phrase in either language when it comes to this type of function however as the quantities represented by the relation aren’t that compatible: one is a continuous variable and one is (surely) discrete.

        But now I’m over-thinking it.

        1. If you can locate VCAA’s using “point in time”, please let me know. It’s a pretty useless and misleading idea for continuous distributions, unless one is very careful. And being careful is not VCAA’s strong suit.

  1. Again, the stupid focus on some stupid ‘real-life’ context. The question has to be asked – what’s so wrong about saying here’s a function g, find t for which g is a maximum. Obviously some of the VCAA exam writers were taking a gap year ….

    By the way, at the risk of being off-topic, I’m sure everyone has heard the wonderful news:

    VCAA have at long last made the marking scheme for its exams public. Finally. Unfortunately, it’s not freely available. You have to pay the MAV a sum of money to get access. Apparently the VCAA Assessors are no longer bound by confidentiality and can disclose the marking scheme through the MAV VCAA Exam Solutions. A cosy arrangement where the Assessors get to make extra money, MAV make money and teachers get the VCAA marking scheme. Everyone’s happy.

  2. JF, are these the actual VCAA marking schemes (as provided to examiners) or are they a MAV marking scheme for the VCAA exams? If you’re not sure, that is fine.

    If it is the first option then why does VCAA not just release them? Unlike MAV, VCAA is not an organisation with private membership (to my knowledge anyway…)

    As it stands, it sounds like it may not be the actual marking scheme but an examiners recollection of the scheme. Good enough perhaps, but raises a few more questions than it answers.

    Off topic perhaps, but certainly relevant!

  3. Can everyone please hold your fire on the VCAA solutions thing? It’s too important an issue to be hidden in an off-topic subthread. I’ll set up a post for discussion of this ASAP.

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