Fit an exponential or quadratic model to data

Answer Key - Grade 9 Math Worksheet - Challenge Me

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

1. 1.

   Ren plotted a play ball tossed straight up, and the calculator fit y = -5x² + 16x + 1.5. At what x does the model reach its highest value?

   1.6
2. 2.

   Tala plotted a water rocket's height, and the calculator fit y = -5x² + 26x + 1. At what x does the model reach its highest value?

   2.6
3. 3.

   Zee plotted visitors inside the science museum, and the calculator fit y = -2.5x² + 23x + 8. At what x does the model reach its highest value?

   4.6
4. 4.

   Ari plotted bean plant growth against plant food, and the calculator fit y = -0.6x² + 7.8x + 4. At what x does the model reach its highest value?

   6.5
5. 5.

   The calculator's fit, rounded: y = 30(1.4)^x. Bo recorded duckweed spreading on the class pond, and the calculator fit y = 30(1.4)^x. In which whole week does the model first go above 200?

   6
6. 6.

   The calculator's fit, rounded: y = 15(1.7)^x. Esme recorded fruit flies in the science-class jar, and the calculator fit y = 15(1.7)^x. In which whole day does the model first go above 400?

   7
7. 7.

   The calculator's fit, rounded: y = 300(0.8)^x. Kira recorded a wet beach towel drying in the sun, and the calculator fit y = 300(0.8)^x. In which whole hour does the model first go below 30?

   11
8. 8.

   Luz plotted algae growing in a fishbowl, and the calculator fit y = 20(1.5)^x. Should Luz trust the model's prediction for x = 30?

   • No: a model can never be used to predict.
   • Yes: the model predicts about 3,835,021, so that is what will happen at that point.
   • No: x = 30 is far outside the data, 0 to 6, so the model may not hold there.
9. 9.

   Milo plotted a water rocket's height, and the calculator fit y = -4.9x² + 29.4x + 1.5. Should Milo trust the model's prediction for x = 12?

   • Yes: the model predicts about -351, so that is what will happen at that moment.
   • No: x = 12 is far outside the data, 0 to 5, so the model may not hold there.
   • No: a model can never be used to predict.
10. 10.

    Noah plotted visitors inside the science museum, and the calculator fit y = -3x² + 28x + 9. Should Noah trust the model's prediction for x = 4.5?

    • No: there is no dot at x = 4.5, so the model cannot be trusted there.
    • Yes: x = 4.5 is inside the data, where the model fits the dots well.
    • No: a model can never be used to predict.