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Name _______________________________________Date________Period____________ Exponential Decay In the activity on exponential growth, you read about the ballots that Alejandro was making for an election. Recall that Alejandro cut a sheet of paper in half, stacked the two pieces and cut them in half, and then stacked the resulting four pieces and cut them in half. In the activity on exponential growth, you investigated the pattern in the number of ballots created by each cut. In this activity, you will look at the pattern in the areas of the ballots. 1. The sheet of paper Alejandro started with had an area of 64 in2. Complete the table below to show the area of a ballot after each of the first 10 cuts. Graph the data from the table on the grid. Be sure to label the grid and mark the scale. #Cuts Area (sq in) 0 64 1 32 2 16 3 4 5 6 7 8 9 10 2. How does the area of a ballot change with each cut? 3. How is the pattern of change in the area different from the exponential growth pattern that you saw in the previous lesson? 4. What is the initial amount (I)? __________________ 5. What is the decay factor (D)? __________________ 6. What is the exponent (x)? ____________________ 7. Write an equation that represents the table.______________________________ (y = I * D x) 8. 20 cuts would result in an area of ___________________ in2 (show your work) 9. 30 cuts would result in an area of in2 (show your work) Name _______________________________________Date________Period____________ Exponential Decay Practice x 1 1. For the equation y 2 Generate a table a. How does the value of y change as x increases? x y 0 1 2 b. Find the value of y when x = 20. 3 4 2. For the equation y = (2)x Generate a table a. How does the value of y change as x increases? x y 0 1 2 b. Find the value of y when x = 20. 3 4 3. a. How are tables of exponential growth and exponential decay relationships different? b. How are they the same? 4. a. How are the graphs of exponential growth and exponential decay functions different? b. How are they the same? x 1 5. In the equation y 24 2 a. What is the decay factor? b. What is the initial amount? 6. Use the table below a. Is the equation exponential or linear? x y 1 20 2 15 b. How can you tell? 3 10 4 5 5 0 c. Write an equation that represents the table. 7. Use the table below a. Is the equation exponential or linear? x y 1 625 2 125 b. How can you tell? 3 25 4 5 5 1 c. Write an equation that represents the table. 8. Use the table below a. What is the initial amount? x y 0 81 1 27 b. What is the decay factor? 2 9 3 3 4 1 c. What is the exponent? d. Write an equation that represents the table. 9. Use the table below x y a. What is the initial amount? 1 256 2 64 3 16 b. What is the decay factor? 4 4 5 1 c. What is the exponent? d. Write an equation that represents the table. 10. Use the table below a. What is the initial amount? x y 1 1296 b. What is the decay factor? 2 216 3 36 4 6 c. What is the exponent? 5 1 d. Write an equation that represents the table.