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
   • 400 bacteria
   • 150 bacteria
   • 250 bacteria
3. 2.

   Bo reads the table. The count doubles each hour. After how many hours does it first pass 1000?

   • 6 hours, 640 bacteria
   • 5 hours, 320 bacteria
   • 7 hours, 1280 bacteria
   • 100 hours, 1010 bacteria

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

   week	seedlings
   0	40
   1	60
   2	?
   3	?

5. 3.

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

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

6. 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

7. 4.

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

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

8. 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	?

9. 5.

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

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

10. Seedlings in one plot (model data)

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

11. 6.

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

    • 20 seedlings
    • 25 seedlings
    • 5 seedlings
    • 10 seedlings
12. 7.

    Milo reads the graph. Which statement about the two ponds is true?

    • The ponds share one carrying capacity, since the plants are the same kind
    • Pond A has the higher carrying capacity, since it levels off first
    • Pond B has the higher carrying capacity, near 100
    • Pond A has the higher carrying capacity, since it starts with more
13. 8.

    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 will catch up, since both keep climbing at the same pace
    • 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

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

    season	carrying capacity (birds)
    summer	400
    winter	150

15. 9.

    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 the count at the start of the year, 400 birds
    • It is fixed for the species, 400 birds, in any season
    • It is larger in winter, because fewer birds are there
16. 10.

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

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