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	10
   1	20
   2	40
   3	80
   4	160

2. 1.

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

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

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

5. 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	?

6. 3.

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

   • 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
   • About 0 frogs, because there is no room to add more

7. Seedlings in one plot (model data)

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

8. 4.

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

   • 10 seedlings
   • 20 seedlings
   • 5 seedlings
   • 25 seedlings
9. 5.

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

   • Pond A has the higher carrying capacity, since it starts with more
   • The ponds share one carrying capacity, since the plants are the same kind
   • Pond B has the higher carrying capacity, near 100
   • Pond A has the higher carrying capacity, since it levels off first
10. 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 is at the carrying capacity of 128, which allows more
    • Line B's resources run short, so it slows toward 60 while Line A doubles
    • Line B will catch up, since both keep climbing at the same pace
    • Line A adds the same number each day, so it climbs faster
11. 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 7 to 9 gained more, since the count is larger
    • Years 2 to 4 gained more, 66 against 3
    • Years 7 to 9 gained more, 150 against 114

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

    season	carrying capacity (birds)
    summer	400
    winter	150

13. 8.

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

    • It is fixed for the species, 400 birds, in any season
    • It is larger in winter, because fewer birds are there
    • It changes with the season, because the resources the field offers change
    • It is the count at the start of the year, 400 birds
14. 9.

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

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

15. 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

16. 10.

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

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