TOOTHPICKS AND FERRIS WHEELS In this task there are two situations: one dealing with counting toothpicks and the other dealing with a Ferris wheel. The ultimate goal in each situation is to model the situation with the appropriate function. Answer them to the best of your ability. 1) In this problem we are creating triangular toothpick patterns. Shown below are the first three triangular patterns made with toothpicks: n = 1 1 =2 1=3 # small # toothpicks Total # of a) From a physical standpoint, what does the triangles Added to toothpicks value of n represent? previous case b) Complete the table. 3 c) Determine the type of relationship n has 4 6 9 with each of the other 3 columns (ie linear, quadratic, exponential etc). Justify your answer. d) Would these be discrete or continuous relationships? Justify your answer. e) Determine whether the 3" column (# of toothpicks added) is arithmetic, geometric, or neither. Justify your answer. f) Model the 4" column (Total # of toothpicks) with a recursive relationship with t, = 3 g) Model the 4" column with regression software (hint: refer to the Curve Expert tutorial in Unit 4 Activity 5) or a graphing calculator. h) Determine the domain and range of your model i) Predict the number of toothpicks needed to make a triangle with 100 toothpicks on one side. Show your work. j) If you only had 300 toothpicks. What would the side length of the biggest triangle you could make be? Show your work