Graph the natural logarithm of the number N of dice remaining after each throw against the number n of the throw and determine the half-life.

This activity simulates the statistical decay of radioactive nuclei. Packages of 100 dice can be purchased online. (a) First, think about the following procedure, but don’t do it yet: Put 100 dice in a bag and shake for a few seconds. Roll out the dice on a tabletop. Each such roll of the dice will represent one time interval Dt. Remove all the dice showing a one on the upper face, and set them aside. Record the remaining number N of dice. Put the remaining dice back in the bag, shake, and roll out again. Repeat this procedure, always removing the dice showing a number one from those on the table, until only a few dice remain. Second, after thinking about this procedure, predict the half-life of the procedure: the number of throws after which half the dice remain when the dice with a one showing have been removed. (b) Finally, perform the activity and record the results. Graph the natural logarithm of the number N of dice remaining after each throw against the number n of the throw and determine the half-life. Compare to your theoretical prediction.