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(i) Write an equation for… (Class 12 Biology 2025, Q33b)

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BiologyCBSE Class 12 · Board exam 2025, set 57/7/1 · 5 marks · Long answer

CBSE Class 12 Biology 2025: question 33(b)

Set in the CBSE Class 12 board exam of 2025, paper 57/7/1, section E, question 33(b), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q33(b) · 5 marks · Long answerOrganisms and Populations

(i) Write an equation for Verhulst-Pearl Logistic Growth Curve where :
N = Population density at time 't'
r = Intrinsic rate of natural increase
(ii) Draw a graph for a population whose population density has reached carrying capacity.
(iii) Draw a growth curve where resources are non-limiting to growth of population.
(iv) Which growth curve is considered more realistic and why ? Explain.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 57/7/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

The logistic equation is the exponential equation dN/dt = rN multiplied by a factor that involves K.

Hint 2

When resources are limited, growth slows as N gets close to K. What shape does that give the curve? What shape does it take when resources are unlimited?

Hint 3

Ask yourself whether any real habitat can supply resources without limit.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

  1. (i) Verhulst-Pearl logistic growth equation:

    Here is the population density at time , is the intrinsic rate of natural increase and is the carrying capacity.

    1 mark

  2. (ii) Draw a sigmoid (S-shaped) curve, with time (t) on the x-axis and population density (N) on the y-axis.

    • The curve begins with a slow lag phase.
    • It then rises steeply in the exponential phase.
    • It finally flattens into a plateau at a horizontal dashed line marked K (carrying capacity).
    1 mark

  3. (iii) Draw a J-shaped curve (exponential growth), with the same axes: time (t) on the x-axis and population density (N) on the y-axis.

    • The curve rises ever more steeply with no upper limit.
    • It follows , because resources are unlimited.
    1 mark

  4. (iv) The logistic (sigmoid) growth curve is considered more realistic.

    1 mark

  5. Reason: No habitat has unlimited resources. Each habitat can support only a maximum number of individuals, its carrying capacity (K). As N approaches K, competition for limited resources slows growth until it levels off, so growth cannot stay exponential for ever.

    1 mark

Answer: (i) dN/dt = rN[(K − N)/K]; (ii) sigmoid (S-shaped) curve levelling off at K; (iii) J-shaped exponential curve; (iv) the logistic (sigmoid) curve is more realistic because resources are always limited and every habitat has a carrying capacity beyond which the population cannot grow.

Where the marks are

  • Writes the correct logistic equation dN/dt = rN(K−N)/K (1 mark)
  • Draws a sigmoid curve reaching a plateau at K, with labelled axes (1 mark)
  • Draws a J-shaped curve for unlimited resources, with labelled axes (1 mark)
  • States that the logistic or sigmoid curve is more realistic (1 mark)
  • Gives the reason: resources are limited and the habitat has a carrying capacity, beyond which growth stops (1 mark)

Revise the chapter

Practise this chapterBoard-style questions from Organisms and Populations, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 57/7/1: every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.