Ερώτηση για το Bitcoin στην εξεταστική της Δευτεροβάθμιας εκπαίδευσης στην Ολλανδία
Ερώτηση για το Bitcoin περιείχαν οι τελικές εξετάσεις των μαθηματικών για την αποφοίτηση στην Δευτεροβάθμια εκπαίδευση στην Ολλανδία. Συγκεκριμένα έπρεπε να υπολογίσουν τον αριθμό των Bitcoin που θα εξορυχτούν μέσα σε ένα χρονικό διάστημα σε συνάρτηση με την αύξηση του βαθμού δυσκολίας στο mining.
Η ερώτηση είναι η εξής έτσι όπως μεταφράστηκε στο σχετικό νήμα στο reddit από ένα ανώνυμο μέλος.
Bitcoin is a digital currency that only exists online. It exists since January 1 2009 and can be used to pay in webshops or for other online services.
Unlike regular money, Bitcoins aren’t put into circulation by a central bank. Instead of that, all Bitcoins are created by making computers solve mathematical problems. It goes like this: Anyone can run special software on their computer that helps solve the problem. The owner of the computer that solves the problem receives 25 (newly created) Bitcoins as a reward. In 2014 approximately every 10 minutes one of these problems was solved, creating 25 more bitcoins every 10 minutes.
On January 1st 2014 about 12.2 million bitcoins had been created.
(3 points) 7. Calculate using these numbers when the number of Bitcoins in circulation rises above 18 million if the rate at which Bitcoins are created does not change.
In reality, the rate at which Bitcoins are created does change. It goes down slowly. During the first four years, January 1st 2009 until January 1st 2013, the reward was 50 bitcoins per solution. The reward for finding a solution is halved every four years: From January 1st 2013 until January 1st 2017 the reward is 25 Bitcoins, the four years after that 12.5, etcetera.
(4 points) 8. Calculate from which year the reward for solving a problem is less than 1 Bitcoin.
The total number of Bitcoins that can ever be created is capped. This is a result of (among other things) the halving of the reward. The total amount of Bitcoins that is in circulation can be approximated using this formula:
C = 21 – 21 * 0.50.25*t
Here, C represents the total number of Bitcoins in millions and t is the time in years, with t=0 representing January 1st 2009.
(3 points) 9. Rationalize the maximum amount of Bitcoins that will ever be in circulation using this formula.
To regulate the number of Bitcoins in circulation, the reward is not only reduced, but the difficulty of the mathematical problems is also increased. This because there are ever more people adding their computer to the Bitcoin network. The difficulty level of the problems goes up exponentially using the formula D = 3.65 * e0.533*t .
Here D is the difficulty value, t is the time in months since January 1st 2013. The higher D, the harder it is to solve the mathematical problem.
(4 points) 10. Calculate the derivative of D and reason how this formula shows that the graph of D is increasingly ascendant.
The formula can be rewritten in such a way that you can enter the difficulty rating D, calculating the number of months until that difficulty rating is met.
Rewrite the formula D = 3.65 * e0.533*t so t is expressed as a function of D.