Carrying capacity: J-shaped and S-shaped growth

Grade 9 Science Worksheet - Challenge Me

Circle the best answer.

1. 1.

   Ari reads the graph and uses growth = r × N × (K − N) ÷ K with r = 0.5. How many ducks are added in the year after year 3?

   • 15 ducks
   • 60 ducks
   • 30 ducks
   • 120 ducks

2. Read this first

   Three groups of plants with the same rate (model data)

   group	count now (N)	carrying capacity (K)
   A	20	200
   B	100	200
   C	180	200

3. 2.

   Bo reads the table. Each group uses growth = r × N × (K − N) ÷ K with r = 0.5. Which group adds the most this year?

   • Groups A and C tie, each adding 9
   • Group B, because 100 is half of 200
   • Group C, because it has the most plants
   • Group A, because it has the most room left, 180

4. Bacteria in a flask that holds 1000 (model data)

   hour	bacteria
   0	50
   1	100
   2	200
   3	400

5. 3.

   Esme reads the table. The count doubles each hour. In which hour would doubling first pass the flask's carrying capacity of 1000?

   • Hour 20, when the count would be 1050
   • Hour 6, when the count would be 3200
   • Hour 5, when the count would be 1600
   • Hour 4, when the count would be 800
6. 4.

   Jun reads the graph. The count passes the carrying capacity at year 4, then falls back. What explains the fall?

   • Growth has no limit, so the fall must be a mistake in the data
   • Growth is fastest at the carrying capacity, so the count bounces off it
   • Above the carrying capacity more are lost than added, so the count falls back toward it
   • The carrying capacity rose to 112 and then dropped back to 100

7. Plants in a field with a carrying capacity of 500 (model data)

   count now (N)	room left, (K − N) ÷ K
   5	0.99
   100	0.8
   250	0.5
   400	0.2
   475	0.05
   500	0

8. 5.

   Kira reads the table. What does the room-left column show about growth as the count rises?

   • Growth is fastest at 500, where the count is largest
   • Growth speeds up, since the fractions grow as the count grows
   • Growth stays about the same size, since the fractions stay near 1
   • Growth is held back more and more, and it reaches 0 at the carrying capacity
9. 6.

   Luz reads the graph. After a dry year at year 5, the count falls to a new flat level. What explains it?

   • The carrying capacity is the 10 ducks of the start, so it fell back
   • The line must rise again soon, since populations have no limit
   • The dry year lowered the carrying capacity from 120 to 80, and the count followed
   • The carrying capacity is still 120, so the fall is a counting slip

10. Notebook

    Notes on yeast in a test tube (classmate's notebook), 4 lines. Columns: line, entry. Line 1: The yeast start at 10 thousand cells and level off at 80 thousand. Line 2: The carrying capacity is the starting number, 10 thousand. Line 3: Early on, each cell has plenty of room and sugar, so the count climbs quickly. Line 4: Later, growth slows as the sugar is used up.

11. 7.

    Milo reads a classmate's notebook about yeast. Which line has the mistake?

    • Line 4: growth is fastest once the sugar is used up, because the count is highest
    • Line 3: early growth should be slow, since the cells are few and have little room
    • Line 1: the yeast would keep rising past 80 thousand, so the count should not level off
    • Line 2: the carrying capacity is the level where growth stops, 80 thousand

12. Notebook

    Notes on bacteria in a flask (classmate's notebook), 4 lines. Columns: line, entry. Line 1: Start: 20 bacteria in a flask with plenty of food. Line 2: Hour 1: 20 doubled is 40. Line 3: Hour 2: 40 doubled is 80. Line 4: Hour 3: 80 + 40 = 120, adding the same 40 as last time.

13. 8.

    Noah reads a classmate's notebook about bacteria. Which line has the mistake?

    • Line 4: doubling 80 gives 160, not 120
    • Line 2: doubling 20 gives 20 + 20 + 20 = 60
    • Line 3: the count should be 60, adding 20 each hour
    • Line 1: the flask should start with 10 bacteria
14. 9.

    Ren reads the graph. Which claim goes with the right reason?

    • Claim: the frogs will keep rising past 90. Reason: the count is still rising at the end, from 89 to 90
    • Claim: growth is fastest near the carrying capacity. Reason: the count is largest there, 89, so the most are added
    • Claim: growth has slowed near the carrying capacity. Reason: from year 9 to year 10 the gain is 2, against 17 at the steepest
    • Claim: the carrying capacity is 3. Reason: that is the first count on the line, at the start of the graph

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

    hour	bacteria
    0	3
    1	6
    2	12
    3	24

16. 10.

    Zee reads the table. The count keeps doubling. Which claim goes with the right reason?

    • Claim: at hour 6 there are 21 bacteria. Reason: 3 is added 6 times, 3 + 6 × 3
    • Claim: at hour 6 there are 96 bacteria. Reason: 3 is doubled 5 times, 3 × 32
    • Claim: at hour 6 there are 18 bacteria. Reason: 3 times 6 hours
    • Claim: at hour 6 there are 192 bacteria. Reason: 3 is doubled 6 times, 3 × 64