n # small triangles 1 1 >#toothpicks Added to previous case Total # of toothpicks (7) 3 4 3 +3 2 4 25 2 6 97 3 4 9 3 5 1642 12 5 6 5325 6236 15 18 30% H₂ 45 63 th 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 n =2 n = 3 n # small triangles # toothpicks Added to previous case Total # of toothpicks 1 1 - 3 2 4 6 9 3 4 5 6 a) From a physical standpoint, what does the value of n represent? b) Complete the table. c) Determine the type of relationship n has 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 3rd column (# of toothpicks added) is arithmetic, geometric, or neither. Justify your answer. f) Model the 4th column (Total # of toothpicks) with a recursive relationship with t₁ = 3 g) Model the 4th 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.