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. 2.

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

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

   • 100 seedlings
   • 135 seedlings
   • 90 seedlings
   • 120 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 1, the first year
   • Year 9, the year nearest the carrying capacity
   • Year 4, with 103 ducks at the start
   • Year 3, with 56 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 120 frogs, because the count doubles again
   • About 1 frog, the same as the year before
   • About 60 frogs, because growth is fastest at the carrying capacity
   • About 0 frogs, because there is no room to add more

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?

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

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

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

    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, 150 against 114
    • Years 7 to 9 gained more, since the count is larger
    • Years 2 to 4 gained more, 66 against 3
14. 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
    • The plants will keep rising at the same pace beyond 120
    • The carrying capacity is still 80, and the plants simply passed it
    • More water raised the carrying capacity to 120, so the plants level off higher

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 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
    • Waste has no effect: the jars are the same kind of yeast