Carrying capacity: J-shaped and S-shaped growth
Grade 9 Science Worksheet - Challenge Me
Circle the best answer.
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 Bo reads the table. Each group uses growth = r × N × (K − N) ÷ K with r = 0.5. Which group adds the most this year?
- Group A, because it has the most room left, 180
- Group C, because it has the most plants
- Groups A and C tie, each adding 9
- Group B, because 100 is half of 200
Bacteria in a flask that holds 1000 (model data)
hour bacteria 0 50 1 100 2 200 3 400 Esme reads the table. The count doubles each hour. In which hour would doubling first pass the flask's carrying capacity of 1000?
- Hour 6, when the count would be 3200
- Hour 20, when the count would be 1050
- Hour 4, when the count would be 800
- Hour 5, when the count would be 1600
Jun reads the graph. The count passes the carrying capacity at year 4, then falls back. What explains the fall?
- The carrying capacity rose to 112 and then dropped back to 100
- Growth has no limit, so the fall must be a mistake in the data
- Above the carrying capacity more are lost than added, so the count falls back toward it
- Growth is fastest at the carrying capacity, so the count bounces off it
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 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 stays about the same size, since the fractions stay near 1
- Growth speeds up, since the fractions grow as the count grows
- Growth is held back more and more, and it reaches 0 at the carrying capacity
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 still 120, so the fall is a counting slip
- 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 the 10 ducks of the start, so it fell back
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.
Milo reads a classmate's notebook about yeast. Which line has the mistake?
- Line 2: the carrying capacity is the level where growth stops, 80 thousand
- Line 1: the yeast would keep rising past 80 thousand, so the count should not level off
- 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
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.
Noah reads a classmate's notebook about bacteria. Which line has the mistake?
- Line 3: the count should be 60, adding 20 each hour
- Line 2: doubling 20 gives 20 + 20 + 20 = 60
- Line 1: the flask should start with 10 bacteria
- Line 4: doubling 80 gives 160, not 120
Notebook
Notes on logistic growth (classmate's notebook), 4 lines. Columns: line, entry. Line 1: Early on, N is small and K − N is large, so growth is almost J-shaped. Line 2: Near K, the fraction (K − N) ÷ K is close to 0, so growth slows. Line 3: So growth is fastest when N reaches K. Line 4: At N = K, the count stays near K.
Pia reads a classmate's notebook about logistic growth. Which line has the mistake?
- Line 4: at N = K the count keeps climbing
- Line 2: near K the fraction is close to 1, so growth speeds up
- Line 3: at N = K the fraction is 0, so growth is 0
- Line 1: early growth is slow and straight, not J-shaped
Ren reads the graph. Which claim goes with the right reason?
- Claim: growth is fastest near the carrying capacity. Reason: the count is largest there, 89, so the most are added
- Claim: the carrying capacity is 3. Reason: that is the first count on the line, at the start of the graph
- 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 frogs will keep rising past 90. Reason: the count is still rising at the end, from 89 to 90
Two ponds of duckweed (model data)
pond plants at the start plants at the flat part weeks to reach half of the flat part A 20 400 6 B 20 250 3 Tala reads the table. Which claim goes with the right reason?
- Claim: the ponds share a carrying capacity. Reason: both hold the same plant
- Claim: pond A has the higher carrying capacity. Reason: it levels off at 400, against 250
- Claim: pond B has the higher carrying capacity. Reason: it reached half of its flat part sooner, in 3 weeks
- Claim: the ponds share a carrying capacity. Reason: each began with 20 plants