Carrying capacity: J-shaped and S-shaped growth
Grade 9 Science Worksheet - Building Confidence

Circle the best answer.
Ari reads the graph. Which words describe the shape of the line?
- Straight: the same number is added each day
- J-shaped: it climbs faster and faster
- Flat: the number stays near one height
- S-shaped: it climbs, then levels off
Bo reads the graph. Which words describe the shape of the line?
Yeast in a test tube (model data). Time (hours) across, 0 to 10, a mark every 2. Yeast cells (thousands) up, 0 to 100, a mark every 20. Yeast cells joins (0, 10), (1, 21), (2, 37), (3, 54), (4, 67), (5, 74), (6, 78), (7, 79), (8, 80), (9, 80), (10, 80) with straight pieces. Yeast in a test tube (model data). Time (hours) across, 0 to 10, a mark every 2. Yeast cells (thousands) up, 0 to 100, a mark every 20. Yeast cells joins (0, 10), (1, 21), (2, 37), (3, 54), (4, 67), (5, 74), (6, 78), (7, 79), (8, 80), (9, 80), (10, 80) with straight pieces. Yeast in a test tube (model data) 0 2 4 6 8 10 0 20 40 60 80 100 Time (hours) Yeast cells (thousands) Yeast cells - J-shaped: it climbs faster and faster to the end
- S-shaped: it speeds up, then levels off
- Straight: the same number is added each hour
- Falling: the number gets smaller each hour
Esme reads the graph. Room and food stay plentiful for one group. Which line fits that group?
Two groups of duckweed (model data). Time (days) across, 0 to 5, a mark every 1. Plants (number) up, 0 to 80, a mark every 20. Line A joins (0, 2), (1, 4), (2, 8), (3, 16), (4, 32), (5, 64) with straight pieces. Line B joins (0, 2), (1, 6), (2, 14), (3, 29), (4, 44), (5, 54) with straight pieces. Two groups of duckweed (model data). Time (days) across, 0 to 5, a mark every 1. Plants (number) up, 0 to 80, a mark every 20. Line A joins (0, 2), (1, 4), (2, 8), (3, 16), (4, 32), (5, 64) with straight pieces. Line B joins (0, 2), (1, 6), (2, 14), (3, 29), (4, 44), (5, 54) with straight pieces. Two groups of duckweed (model data) 0 1 2 3 4 5 0 20 40 60 80 Time (days) Plants (number) Line A Line B - Line B, because it levels off, which shows room and food are plentiful
- Neither line, because plentiful food gives a flat line
- Line B, because it has more plants on day 3, 29 against 16
- Line A, because it is J-shaped
Jun reads the graph. What is the carrying capacity of the pond?
Frogs in a pond (model data). Time (years) across, 0 to 7, a mark every 1. Frogs (number) up, 0 to 80, a mark every 20. Frogs joins (0, 6), (1, 14), (2, 27), (3, 41), (4, 52), (5, 57), (6, 59), (7, 60) with straight pieces. Carrying capacity joins (0, 60), (7, 60) with a straight piece. Frogs in a pond (model data). Time (years) across, 0 to 7, a mark every 1. Frogs (number) up, 0 to 80, a mark every 20. Frogs joins (0, 6), (1, 14), (2, 27), (3, 41), (4, 52), (5, 57), (6, 59), (7, 60) with straight pieces. Carrying capacity joins (0, 60), (7, 60) with a straight piece. Frogs in a pond (model data) 0 1 2 3 4 5 6 7 0 20 40 60 80 Time (years) Frogs (number) Frogs Carrying capacity - 7 frogs
- 80 frogs
- 6 frogs
- 60 frogs
Pia reads the graph. What does the duck line do after it reaches the carrying capacity line?
Ducks on an island (model data). Time (years) across, 0 to 8, a mark every 1. Ducks (number) up, 0 to 60, a mark every 20. Ducks joins (0, 4), (1, 9), (2, 16), (3, 25), (4, 32), (5, 36), (6, 38), (7, 39), (8, 40) with straight pieces. Carrying capacity joins (0, 40), (8, 40) with a straight piece. Ducks on an island (model data). Time (years) across, 0 to 8, a mark every 1. Ducks (number) up, 0 to 60, a mark every 20. Ducks joins (0, 4), (1, 9), (2, 16), (3, 25), (4, 32), (5, 36), (6, 38), (7, 39), (8, 40) with straight pieces. Carrying capacity joins (0, 40), (8, 40) with a straight piece. Ducks on an island (model data) 0 1 2 3 4 5 6 7 8 0 20 40 60 Time (years) Ducks (number) Ducks Carrying capacity - It climbs fastest there
- It keeps climbing in a J-shape
- It drops back to the first count
- It stays close to the carrying capacity line
Read this first
Bacteria in a flask with plenty of food (model data)
hour bacteria 0 50 1 100 2 200 3 ? Ren reads the table. The count doubles each hour. How many bacteria are there at hour 3?
- 300 bacteria
- 400 bacteria
- 800 bacteria
- 600 bacteria
Duckweed on a pond (model data)
day plants 0 4 1 8 2 16 3 32 Tala reads the table. How many plants were added between day 2 and day 3?
- 16 plants
- 32 plants
- 4 plants
- 8 plants
Milo reads the graph. Why does the line flatten near the carrying capacity?
Duckweed on a small pond (model data). Time (days) across, 0 to 12, a mark every 2. Duckweed plants (number) up, 0 to 120, a mark every 20. Duckweed plants joins (0, 5), (1, 10), (2, 21), (3, 37), (4, 56), (5, 74), (6, 86), (7, 93), (8, 97), (9, 99), (10, 99), (11, 100), (12, 100) with straight pieces. Carrying capacity joins (0, 100), (12, 100) with a straight piece. Duckweed on a small pond (model data). Time (days) across, 0 to 12, a mark every 2. Duckweed plants (number) up, 0 to 120, a mark every 20. Duckweed plants joins (0, 5), (1, 10), (2, 21), (3, 37), (4, 56), (5, 74), (6, 86), (7, 93), (8, 97), (9, 99), (10, 99), (11, 100), (12, 100) with straight pieces. Carrying capacity joins (0, 100), (12, 100) with a straight piece. Duckweed on a small pond (model data) 0 2 4 6 8 10 12 0 20 40 60 80 100 120 Time (days) Duckweed plants (number) Duckweed plants Carrying capacity - Nothing limits the plants, so the flat part is a graph slip
- Duckweed has a fixed limit of 100 on any pond
- Space and light get short as the plants crowd, so growth slows
- The plants stop growing once they are old
Yeast in a test tube with a fixed amount of sugar (model data)
hour yeast cells (thousands) sugar left (grams) 0 4 100 1 10 85 2 22 60 3 34 25 4 38 8 5 38 2 Noah reads the table. What change in the table explains why the yeast count levels off?
- The sugar left stays high, so food is not short
- The sugar left falls from 100 to 2 grams, so the yeast run low on food
- The yeast count rises from 4 to 38, so the sugar grows too
- Yeast settle at 38 thousand cells in any test tube
Kira reads the graph. In weeks 0 to 3 the line climbs a bit more each week. Why?
Sunflower seedlings in a plot (model data). Time (weeks) across, 0 to 8, a mark every 1. Seedlings (number) up, 0 to 100, a mark every 20. Seedlings joins (0, 8), (1, 16), (2, 28), (3, 44), (4, 59), (5, 69), (6, 74), (7, 77), (8, 79) with straight pieces. Carrying capacity joins (0, 80), (8, 80) with a straight piece. Sunflower seedlings in a plot (model data). Time (weeks) across, 0 to 8, a mark every 1. Seedlings (number) up, 0 to 100, a mark every 20. Seedlings joins (0, 8), (1, 16), (2, 28), (3, 44), (4, 59), (5, 69), (6, 74), (7, 77), (8, 79) with straight pieces. Carrying capacity joins (0, 80), (8, 80) with a straight piece. 0 1 2 3 4 5 6 7 8 0 20 40 60 80 100 Time (weeks) Seedlings (number) Seedlings Carrying capacity - The count is nearest its limit, so growth is fastest
- The seedlings are already at the carrying capacity
- Few seedlings share plenty of room and light, so growth is almost J-shaped
- Each week the same number of seedlings is added