Carrying capacity: J-shaped and S-shaped growth

Grade 9 Science Worksheet

Circle the best answer.

1. Read this first

   Bacteria in a flask with plenty of food (model data)

   hour	bacteria
   0	25
   1	50
   2	100

2. 1.

   Ari reads the table. The count doubles every hour. How many bacteria are there after 5 hours?

   • 800 bacteria
   • 250 bacteria
   • 400 bacteria
   • 150 bacteria

3. Seedlings in a plot that grow 50 percent each week (model data)

   week	seedlings
   0	40
   1	60
   2	?
   3	?

4. 2.

   Esme reads the table. Each week the count is multiplied by 1.5. What number goes in the week 3 row?

   • 135 seedlings
   • 100 seedlings
   • 90 seedlings
   • 120 seedlings

5. Ducks on a lake with a carrying capacity of 200 (model data)

   year	ducks at the start	ducks added
   1	10	15
   2	25	31
   3	56	47
   4	103	45
   5	148	29
   6	177	14
   7	191	6
   8	197	2
   9	199	1

6. 3.

   Jun reads the table. In which year were the most ducks added?

   • Year 3, with 56 ducks at the start
   • Year 9, the year nearest the carrying capacity
   • Year 4, with 103 ducks at the start
   • Year 1, the first year

7. Frogs in a pond with a carrying capacity of 120 (model data)

   year	frogs at the start	frogs added
   1	6	10
   2	16	23
   3	39	32
   4	71	26
   5	97	14
   6	111	6
   7	117	2
   8	119	1
   9	120	?

8. 4.

   Kira reads the table. In year 9 the pond already holds 120 frogs. About how many frogs are added in year 9?

   • About 0 frogs, because there is no room to add more
   • About 1 frog, the same as the year before
   • About 60 frogs, because growth is fastest at the carrying capacity
   • About 120 frogs, because the count doubles again

9. Seedlings in one plot (model data)

   carrying capacity (K)	count now (N)	rate per seedling (r)
   100	50	0.4

10. 5.

    Luz uses growth = r × N × (K − N) ÷ K. How many seedlings are added in one year?

    • 5 seedlings
    • 10 seedlings
    • 25 seedlings
    • 20 seedlings
11. 6.

    Noah reads the graph, which marks the carrying capacity for Line B. Why is Line B far below Line A on day 6?

    • Line A adds the same number each day, so it climbs faster
    • Line B's resources run short, so it slows toward 60 while Line A doubles
    • Line A is at the carrying capacity of 128, which allows more
    • Line B will catch up, since both keep climbing at the same pace
12. 7.

    Pia reads the graph. Compare the gain from year 2 to year 4 with the gain from year 7 to year 9.

    • The gains are equal, since the same number is added in any two years
    • Years 2 to 4 gained more, 66 against 3
    • Years 7 to 9 gained more, 150 against 114
    • Years 7 to 9 gained more, since the count is larger

13. Birds in one field in two seasons (model data)

    season	carrying capacity (birds)
    summer	400
    winter	150

14. 8.

    Ren reads the table. What does it show about the carrying capacity of the field?

    • It changes with the season, because the resources the field offers change
    • It is larger in winter, because fewer birds are there
    • It is the count at the start of the year, 400 birds
    • It is fixed for the species, 400 birds, in any season
15. 9.

    Tala reads the graph. Extra water was added at week 10. What does the second flat part show?

    • Water changed the plants into a different kind, which changed the curve
    • More water raised the carrying capacity to 120, so the plants level off higher
    • The plants will keep rising at the same pace beyond 120
    • The carrying capacity is still 80, and the plants simply passed it

16. Two jars of yeast (model data)

    jar	waste cleared each day	yeast at the start (thousands)	yeast at the flat part (thousands)
    A	yes	5	120
    B	no	5	70

17. 10.

    Zee reads the table. What does it suggest about waste and the carrying capacity?

    • Waste build-up lowers it: jar B levels off at 70, jar A at 120
    • Waste has no effect: the jars are the same kind of yeast
    • Both jars share a carrying capacity of 5, the same start
    • Waste raises it: jar B has more waste and a lower count