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This is the worksheet that students fill out as they go from one station to the next for the exponential growth and decay stations game.
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Name:_______________Date:________
Exponential Growth and Decay Station GameStation 1
(a) What fraction of the original piece is left after the first tear?
(b) What fraction of the original piece is left after the second tear?
(c) Fill in the table:Number of times cut 0 1 2 3 4
Fraction of original piece left
(d) Write an expression for the fraction of the paper left after t cuts.
(e) If you continue this process, will the paper ever disappear?
Station 2(a) Fill in the table:
Number of iterations 0 1 2 3
Number of identical triangles
1
(b) Write an expression for the number of triangles after n iterations
(c) Fill out the table:Number of iterations 0 1 2 3
Triangle side length 8 inches
(d) Write an expression for the length of the side of a triangle after n iterations
Station 3(a) Fill in the table:
Number of iterations 0 1 2 3 4 5
Number of TOTAL triangles (big and
1 5
small)(b) Write an expression for the number of triangles after n iterations
(c) Is this exponential growth? Explain.
Station 4(a) Fill in the table:
Number of iterations 0 1 2 3 4 5
Number of new circles drawn
1
(b) Write an expression for the number of new circles drawn after n iterations
(c) How many new circles will you need to draw in the 10th iteration?
Station 5(a) Fill in the table:
Number of times all heads have been cut off
0 1 2 3 4 5
Number of total heads 7 14
(b) Write an expression for the number of total heads that the Hydra will have after all its heads have been cut off n times.
(c) Write an expression for the number of total heads that the Hydra will have after h heads have been cut off.