Worksheet

choosing the model that fits the data: linear, quadratic or exponential

Grade 11 Math Worksheet - Building Confidence

NameDate

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

  1. 0 → 15; 1 → 22; 3 → 36; 5 → 50. The weeks are not evenly spaced. Milo records the dollars in a class savings jar on weeks 0, 1, 3 and 5. Which model fits, and what does it do each week?

    • Exponential: the jumps grow from $7 to $14 as the weeks go on
    • Quadratic: the jumps $7, $14 and $14 keep changing
    • Linear: it adds $7 every week

  2. 0 → 400; 1 → 320; 3 → 204.8; 5 → 131.1. Noah tracks a used scooter's value in dollars at years 0, 1, 3 and 5. Which model fits, and what does it do every year?

    • Quadratic: the drops 80, 115.2 and 73.7 keep changing
    • Exponential: the value is multiplied by 0.8 every year
    • Linear: the value drops by 80 every year, so it hits 0 in year 5

  3. 1 → 5; 2 → 10; 3 → 19; 4 → 32; 5 → 49. Pia's patio pattern has 5, 10, 19, 32 and 49 tiles in steps 1 to 5. Which equation fits every step?

    • y = 5(2)^(x − 1)
    • y = 4x² − 7x + 8
    • y = 2x² − x + 4
    • y = 2x² + 3

  4. 0 → 80; 5 → 40; 10 → 20; 15 → 10. Esme measures the grams of dye left in a tank at minutes 0, 5, 10 and 15. Which equation fits every row?

    • y = 80 − 8x
    • y = 80(1/2)^x
    • y = 80(1/2)^(x/5)

  5. 0 → 6; 1 → 54; 2 → 70; 3 → 54; 4 → 6. Zee records a thrown ball's height in feet each second from 0 to 4. Which equation fits every row?

    • y = −32x² + 80x + 6
    • y = 16x² − 64x + 6
    • y = 6 + 48x
    • y = −16x² + 64x + 6

  6. A model for the grams of dye in a tank is P = 800(0.5)^(t/6), with t in days. To the nearest tenth, what percent change per day does Bo read? A decrease is negative.

  7. A model for a town's yearly bike-share rides is y = 250(2)^(x/4), with x in years. To the nearest tenth, what percent change per year does Esme read?

  8. A model for a used car's value in dollars is V = 1,500(0.8)^(t/3), with t in years. To the nearest tenth, what percent change per year does Jun read? A decrease is negative.

  9. Technology fits y = 250(1.06)^x to a town's daily bike-share rides after x years. After how many years does Kira's model reach 400 rides, to the nearest tenth?

  10. Technology fits y = 1,500(0.9)^x to a used car's value in dollars after x years. After how many years does Milo's model fall to $800, to the nearest tenth?

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choosing the model that fits the data: linear, quadratic or exponential

Answer Key - Grade 11 Math Worksheet - Building Confidence

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

  1. 0 → 15; 1 → 22; 3 → 36; 5 → 50. The weeks are not evenly spaced. Milo records the dollars in a class savings jar on weeks 0, 1, 3 and 5. Which model fits, and what does it do each week?

    • Exponential: the jumps grow from $7 to $14 as the weeks go on
    • Quadratic: the jumps $7, $14 and $14 keep changing
    • Linear: it adds $7 every week

  2. 0 → 400; 1 → 320; 3 → 204.8; 5 → 131.1. Noah tracks a used scooter's value in dollars at years 0, 1, 3 and 5. Which model fits, and what does it do every year?

    • Quadratic: the drops 80, 115.2 and 73.7 keep changing
    • Exponential: the value is multiplied by 0.8 every year
    • Linear: the value drops by 80 every year, so it hits 0 in year 5

  3. 1 → 5; 2 → 10; 3 → 19; 4 → 32; 5 → 49. Pia's patio pattern has 5, 10, 19, 32 and 49 tiles in steps 1 to 5. Which equation fits every step?

    • y = 5(2)^(x − 1)
    • y = 4x² − 7x + 8
    • y = 2x² − x + 4
    • y = 2x² + 3

  4. 0 → 80; 5 → 40; 10 → 20; 15 → 10. Esme measures the grams of dye left in a tank at minutes 0, 5, 10 and 15. Which equation fits every row?

    • y = 80 − 8x
    • y = 80(1/2)^x
    • y = 80(1/2)^(x/5)

  5. 0 → 6; 1 → 54; 2 → 70; 3 → 54; 4 → 6. Zee records a thrown ball's height in feet each second from 0 to 4. Which equation fits every row?

    • y = −32x² + 80x + 6
    • y = 16x² − 64x + 6
    • y = 6 + 48x
    • y = −16x² + 64x + 6

  6. A model for the grams of dye in a tank is P = 800(0.5)^(t/6), with t in days. To the nearest tenth, what percent change per day does Bo read? A decrease is negative.

    -10.9

  7. A model for a town's yearly bike-share rides is y = 250(2)^(x/4), with x in years. To the nearest tenth, what percent change per year does Esme read?

    18.9

  8. A model for a used car's value in dollars is V = 1,500(0.8)^(t/3), with t in years. To the nearest tenth, what percent change per year does Jun read? A decrease is negative.

    -7.2

  9. Technology fits y = 250(1.06)^x to a town's daily bike-share rides after x years. After how many years does Kira's model reach 400 rides, to the nearest tenth?

    8.1

  10. Technology fits y = 1,500(0.9)^x to a used car's value in dollars after x years. After how many years does Milo's model fall to $800, to the nearest tenth?

    6