Grade 9 · Science · Biology

9th grade Carrying capacity: J-shaped and S-shaped growth worksheet

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Carrying capacity: J-shaped and S-shaped growth

Grade 9 Science Worksheet - Building Confidence

NameDate

Circle the best answer.

1.
Ari reads the graph. Which words describe the shape of the line?
- J-shaped: it climbs faster and faster
- Straight: the same number is added each day
- S-shaped: it climbs, then levels off
- Flat: the number stays near one height
2.
Bo reads the graph. Which words describe the shape of the line?
- Straight: the same number is added each hour
- J-shaped: it climbs faster and faster to the end
- Falling: the number gets smaller each hour
- S-shaped: it speeds up, then levels off
3.
Jun reads the graph. What is the carrying capacity of the pond?
- 6 frogs
- 80 frogs
- 60 frogs
- 7 frogs
Read this first
Snails in a garden tank (model data)
week snails
0 4
1 9
2 17
3 28
4 38
5 44
6 48
7 49
8 50
4.
Luz reads the table. About what carrying capacity does the tank show?
- 4 snails
- 100 snails
- 50 snails
- 8 snails
5.
Pia reads the graph. What does the duck line do after it reaches the carrying capacity line?
- It stays close to the carrying capacity line
- It keeps climbing in a J-shape
- It drops back to the first count
- It climbs fastest there
Bacteria in a flask with plenty of food (model data)
hour bacteria
0 50
1 100
2 200
3 ?
6.
Ren reads the table. The count doubles each hour. How many bacteria are there at hour 3?
- 300 bacteria
- 800 bacteria
- 400 bacteria
- 600 bacteria
Duckweed on a pond (model data)
day plants
0 4
1 8
2 16
3 32
7.
Tala reads the table. How many plants were added between day 2 and day 3?
- 32 plants
- 4 plants
- 16 plants
- 8 plants
Three groups of bacteria (model data)
group day 0 day 1 day 2 day 3
A 10 20 30 40
B 10 20 40 80
C 10 30 90 270
8.
Zee reads the table. Which group doubles each day?
- Group A, because it goes up by 10 a day
- Group A and Group B, because both have 20 on day 1
- Group B, because 20, 40 and 80 each double
- Group C, because it triples, 30 to 90 to 270
9.
Milo reads the graph. Why does the line flatten near the carrying capacity?
- Duckweed has a fixed limit of 100 on any pond
- The plants stop growing once they are old
- Space and light get short as the plants crowd, so growth slows
- Nothing limits the plants, so the flat part is a graph slip
10.
Kira reads the graph. In weeks 0 to 3 the line climbs a bit more each week. Why?
- The seedlings are already at the carrying capacity
- The count is nearest its limit, so growth is fastest
- Few seedlings share plenty of room and light, so growth is almost J-shaped
- Each week the same number of seedlings is added

week	snails
0	4
1	9
2	17
3	28
4	38
5	44
6	48
7	49
8	50

hour	bacteria
0	50
1	100
2	200
3	?

day	plants
0	4
1	8
2	16
3	32

group	day 0	day 1	day 2	day 3
A	10	20	30	40
B	10	20	40	80
C	10	30	90	270

9th grade Carrying capacity: J-shaped and S-shaped growth worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Carrying capacity and growth curves: J-shaped and S-shaped growth, doubling, and the carrying-capacity line. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can tell a J-shaped line (the count is multiplied by the same number each step, so the number added grows) from an S-shaped line (it speeds up, slows, then levels off).
I can read the carrying capacity off a graph (the height of the "carrying capacity" line, where the population line levels off) or off a table (the count that stops changing), and not mistake it for the starting count.
I can double a count several times, find the number added in one step, find when a doubling count first passes a limit, and use a percent growth as a multiplier.
I can say why growth slows near K: space, light, food and other resources become short as the population crowds.
I can use growth = r × N × (K − N) ÷ K: N small gives almost r × N, and N = K gives 0.
I can see in a table of gains that growth is greatest in the middle of the climb and shrinks toward 0 at K.

Standard: HS-LS2-1

Words to know

exponential growth: The count is multiplied by the same number each step, so the number added grows.

J-shaped curve: The graph of exponential growth: it climbs faster and faster.

logistic growth: Growth that slows as resources become short and levels off.

S-shaped curve: The graph of logistic growth: it speeds up, slows, then flattens.

carrying capacity (K): The largest count of one kind that a place can support.

resource: Something a living thing needs, such as food, water, space or light.

doubling: The count is multiplied by 2 each step.

per-individual rate (r): How fast each individual adds to the count when nothing holds growth back.

Common mistakes

Your child thought the population keeps growing with no limit. Food, space and light run short, so growth slows and levels off at the carrying capacity. Ask your child, 'What would run short first?'

Your child read the starting number as the carrying capacity. The carrying capacity is the most the place can support, where the line levels off. Ask your child, 'Where does the line go flat?'

Your child thought growth is fastest at the carrying capacity. Growth is greatest in the middle of the climb and shrinks to about 0 at the top. Ask your child, 'How many are added at the top?'

Questions parents ask

What is the most common mistake with carrying capacity: j-shaped and s-shaped growth?

Your child thought the population keeps growing with no limit. Food, space and light run short, so growth slows and levels off at the carrying capacity. Ask your child, 'What would run short first?'

Are these 9th grade science worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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9th grade Carrying capacity: J-shaped and S-shaped growth worksheet

Snails in a garden tank (model data)

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

Duckweed on a pond (model data)

Three groups of bacteria (model data)