Linear, quadratic or exponential? And which grows faster in the end?

Answer Key - Grade 9 Math Worksheet - Building Confidence

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

1. Read this first

   Growth table

   x	y
   0	2
   1	6
   2	18
   3	54
   4	162

   Gaps on the arrows: +4, +12, +36, +108. Changes in the gaps: +8, +24, +72. Factors on the arrows: ×3, ×3, ×3, ×3.

2. 1.

   Tala's science club counts duckweed plants in a tank each week. The table already shows the gaps and factors. Is it linear, quadratic or exponential?

   • Linear: equal gaps
   • Quadratic: the gaps change by the same amount
   • Exponential: equal factors

3. Growth table

   x	y
   0	3
   1	4
   2	7
   3	12
   4	19

   Gaps on the arrows: +1, +3, +5, +7. Changes in the gaps: +2, +2, +2. Factors on the arrows: ×4/3, ×7/4, ×12/7, ×19/12.

4. 2.

   Zee builds square block patterns, each with a 3-block tail. The table already shows the gaps and factors. Is it linear, quadratic or exponential?

   • Linear: equal gaps
   • Quadratic: the gaps change by the same amount
   • Exponential: equal factors

5. Growth table

   x	y
   0	5
   1	10
   2	20
   3	40
   4	80

   Gaps on the arrows: +5, +10, +20, +40. Changes in the gaps: +5, +10, +20. Factors on the arrows: ×2, ×2, ×2, ×2.

6. 3.

   Ari keeps cutting paper strips in half and counts the pieces. The table already shows the gaps and factors. Is it linear, quadratic or exponential?

   • Exponential: equal factors
   • Quadratic: the gaps change by the same amount
   • Linear: equal gaps

7. Growth table

   x	y
   0	1
   1	4
   2	11
   3	22
   4	37

   Gaps on the arrows: +3, +7, +11, +15. Changes in the gaps: +4, +4, +4. Factors on the arrows: ×4, ×11/4, ×2, ×37/22.

8. 4.

   Bo draws a star pattern for art club. The table already shows the gaps and factors. Is it linear, quadratic or exponential?

   • Exponential: equal factors
   • Linear: equal gaps
   • Quadratic: the gaps change by the same amount

9. Growth table

   x	y
   0	6
   1	10
   2	14
   3	18
   4	22

   Gaps on the arrows: +4, +4, +4, +4. Changes in the gaps: 0, 0, 0. Factors on the arrows: ×5/3, ×7/5, ×9/7, ×11/9.

10. 5.

    Esme stacks paper cups in rows for a club fair. The table already shows the gaps and factors. Is it linear, quadratic or exponential?

    • Exponential: equal factors
    • Quadratic: the gaps change by the same amount
    • Linear: equal gaps

11. Growth table

    x	y
    0	2
    1	5
    2	12
    3	23

12. 6.

    Luz's ladder-pattern table is quadratic: the gaps grow by 4 each row. What is y at x = 4?

    38
13. 7.

    Milo's flower-pattern table is exponential: every arrow is × 5. What is y at x = 4?

    625

14. Two growth tables, side by side

    x	3x + 4	2^x
    0	4	1
    1	7	2
    2	10	4
    3	13	8
    4	16	16
    5	19	32
    6	22	64

15. 8.

    Noah races two robots. One table is y = 3x + 4; the other is y = 2^x. In the table, what is the first x where 2^x is bigger?

    5
16. 9.

    Pia compares two bike-club step counts. One table is y = 10x + 2; the other is y = 2^x. In the table, what is the first x where 2^x is bigger?

    6
17. 10.

    Ren compares two drum-beat patterns. One table is y = 6x + 9; the other is y = 3^x. In the table, what is the first x where 3^x is bigger?

    4