Fit an exponential or quadratic model to data

Answer Key - Grade 9 Math Worksheet

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

1. 1.

   Ren plotted algae growing in a fishbowl, and the calculator fit y = 30(1.35)^x. What does the model predict for x = 4, to the nearest whole number?

   100
2. 2.

   Tala plotted lily pads spreading on a park pond, and the calculator fit y = 8(1.45)^x. What does the model predict for x = 5, to the nearest whole number?

   51
3. 3.

   Zee plotted a bowl of soup cooling, and the calculator fit y = 62(0.94)^x. What does the model predict for x = 6, to the nearest whole number?

   43
4. 4.

   Bo plotted duckweed spreading on the class pond, and the calculator fit y = 35(1.45)^x. What is the residual for the dot at x = 4, to the nearest tenth?

   -7.7
5. 5.

   Esme plotted a water rocket's height, and the calculator fit y = -4.9x² + 27.5x + 1.5. What is the residual for the dot at x = 3, to the nearest tenth?

   0.5
6. 6.

   Jun plotted how high a play ball bounces back, and the calculator fit y = 120(0.68)^x. What is the residual for the dot at x = 2, to the nearest tenth?

   -3.2
7. 7.

   Kira plotted visitors inside the science museum, and the calculator fit y = -2.5x² + 26x + 12. What is the residual for the dot at x = 5, to the nearest tenth?

   -1.5

8. Read this first

   Table, x | data | line | quadratic

   0 | 2.9 | 13 | 3; 2 | 12.8 | 13 | 13; 4 | 19.9 | 14 | 20; 6 | 22.7 | 14 | 23; 8 | 22 | 15 | 22; 10 | 15.8 | 16 | 17; 12 | 6.5 | 16 | 7. The line is y = 0.3x + 12.6; the quadratic model is y = -0.5x² + 6.4x + 2.5. Predictions are rounded to whole numbers.

9. 8.

   Milo fit a line and a quadratic model to bean plant growth against plant food. The table lists both models' predictions. Which model fits the data better?

   • The quadratic model: its predictions stay close to every dot.
   • The line, because it is closer at x = 10.
   • Both fit equally well.
   • The line, because a line is simpler and easier to read than a curve.

10. Table, x | data | line | exponential

    0 | 6 | -15 | 6; 1 | 10 | 6 | 10; 2 | 18 | 28 | 17; 3 | 29 | 49 | 29; 4 | 47 | 71 | 50; 5 | 95 | 92 | 85; 6 | 139 | 113 | 145. The line is y = 21.4x - 14.9; the exponential model is y = 6(1.7)^x. Predictions are rounded to whole numbers.

11. 9.

    Noah fit a line and an exponential model to lily pads spreading on a park pond. The table lists both models' predictions. Which model fits the data better?

    • The line, because it is closer at x = 5.
    • The line, because a line is simpler and easier to work with than a curve.
    • Both fit equally well.
    • The exponential model: its predictions stay close to every dot.

12. Table, x | data | line | quadratic

    0 | 11 | 39 | 10; 1 | 32 | 41 | 32; 2 | 45 | 44 | 48; 3 | 63 | 46 | 60; 4 | 67 | 49 | 68; 5 | 68 | 51 | 70; 6 | 69 | 53 | 68; 7 | 63 | 56 | 60; 8 | 47 | 58 | 48; 9 | 31 | 61 | 32. The line is y = 2.4x + 38.9; the quadratic model is y = -2.4x² + 24x + 10. Predictions are rounded to whole numbers.

13. 10.

    Pia fit a line and a quadratic model to visitors inside the science museum. The table lists both models' predictions. Which model fits the data better?

    • The line, because it is closer at x = 2.
    • The quadratic model: its predictions stay close to every dot.
    • Both fit equally well.
    • The line, because a line is simpler.