Fit an exponential or quadratic model to data

Answer Key - Grade 9 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. 1.

   Ren plotted duckweed spreading on the class pond, and the calculator fit y = 40(1.5)^x. What does the model predict for x = 3?

   135
2. 2.

   Tala plotted fruit flies in the science-class jar, and the calculator fit y = 25(1.4)^x. What does the model predict for x = 2?

   49
3. 3.

   Zee plotted how high a play ball bounces back, and the calculator fit y = 80(0.7)^x. What does the model predict for x = 2?

   39.2
4. 4.

   Ari plotted a mug of cocoa cooling, and the calculator fit y = 50(0.8)^x. What does the model predict for x = 3?

   25.6
5. 5.

   Bo plotted a water rocket's height, and the calculator fit y = -4.9x² + 28.4x + 1.2. What does the model predict for x = 3?

   42.3
6. 6.

   Esme plotted a bike's stopping distance against its speed, and the calculator fit y = 0.4x² + 1.5x + 2. What does the model predict for x = 8?

   39.6
7. 7.

   Jun plotted bean plant growth against plant food, and the calculator fit y = -0.5x² + 6x + 3. What does the model predict for x = 4?

   19

8. Read this first

   Use the table

   x	y
   0	15
   1	52
   2	79
   3	98
   4	109
   5	115

   Differences: 37, 27, 19, 11, 6. Second differences: -10, -8, -8, -5. Ratios (each y over the one before): 3.47, 1.52, 1.24, 1.11, 1.06.

9. 8.

   Milo recorded visitors inside the science museum and worked out the differences and ratios. Which kind of model fits the data best?

   • Exponential: the differences keep changing from row to row.
   • Linear: the values keep changing.
   • Quadratic: the second differences stay about the same.

10. Use the table

    x	y
    0	30
    1	44
    2	66
    3	99
    4	151
    5	226

    Differences: 14, 22, 33, 52, 75. Second differences: 8, 11, 19, 23. Ratios (each y over the one before): 1.47, 1.5, 1.5, 1.53, 1.5.

11. 9.

    Noah recorded algae growing in a fishbowl and worked out the differences and ratios. Which kind of model fits the data best?

    • Linear: the values keep going up.
    • Quadratic: the differences keep changing as the table goes down.
    • Exponential: the ratios stay about the same.

12. Use the table

    x	y
    2	5
    4	13
    6	25
    8	42
    10	63
    12	89

    Differences: 8, 12, 17, 21, 26. Second differences: 4, 5, 4, 5. Ratios (each y over the one before): 2.6, 1.92, 1.68, 1.5, 1.41.

13. 10.

    Pia recorded a bike's stopping distance against its speed and worked out the differences and ratios. Which kind of model fits the data best?

    • Quadratic: the second differences stay about the same.
    • Exponential: the differences keep changing down the table.
    • Linear: the values keep going up.