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CraftExam
medium difficulty7 min

Exponential and Logistic Population Growth

Population growth models describe how population size changes with time. Exponential growth occurs when resources are unlimited, while logistic growth occurs when resources are limited and population size approaches carrying capacity.

In one line: J means jumping growth; S means slowing near support limit.

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Understand it

  • Population growth depends on births, deaths, immigration and emigration.
  • Under ideal conditions with abundant food and space, a population may show exponential growth, represented by a J-shaped curve.
  • In nature, resources become limiting, so growth slows as population size approaches the carrying capacity, represented by an S-shaped logistic curve.
  • Carrying capacity is the maximum population size that an environment can support sustainably.
  • Examiners often test whether students can connect the equation, curve shape and ecological meaning instead of memorising only symbols.

Example

Bacteria in a fresh nutrient medium may show rapid exponential increase for some time. A deer population in a forest usually follows logistic growth because food, space and predation limit unlimited increase.

Rule to remember

Exponential growth: dN/dt = rN, where N is population size and r is intrinsic rate of natural increase.

Logistic growth: dN/dt = rN(K-N)/K, where K is carrying capacity.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

  1. 1If a population has N = 100 and r = 0.2 per year under ideal conditions, dN/dt = rN = 0.2 × 100 = 20 individuals per year.
  2. 2If resources become limited and the population nears K, logistic growth predicts a slower increase.

Method you can reuse

For a growth model answer: identify whether resources are unlimited or limited, write the correct equation, define N, r and K where applicable, describe the curve shape, and explain what happens as population size increases.

Visual tip

Graph support should include J-shaped exponential curve and S-shaped logistic curve. Labels must include population size, time, carrying capacity K, lag phase, rapid growth phase and slowing phase near K.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Why is logistic growth more realistic than exponential growth for most natural populations?

Think first, then show answer
Logistic growth is more realistic because natural resources such as food, space and shelter are limited. These limits slow population increase as it approaches the environment's carrying capacity.

Common wrong answer

Drawing an S-shaped curve but calling it exponential growth is wrong; exponential growth is J-shaped and assumes unlimited resources.

Don't mix this up

Students often write carrying capacity as the current population size. It is actually the maximum sustainable population size supported by the environment under given conditions.

Exam tip

For graph questions, mention curve shape, resource condition and carrying capacity. For equations, define every symbol and connect it to biological meaning.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Questions may ask for equations, symbol meanings, graph identification, comparison between J-shaped and S-shaped curves, or the ecological importance of carrying capacity.

Answer plan

State the model, write the equation, define all symbols, describe the curve shape, explain the resource condition, and add one ecological example such as bacteria for exponential growth or a forest animal population for logistic growth.
  1. 1

    Enough for 1 mark

    Population growth models describe how population size changes with time. Exponential growth occurs when resources are unlimited, while logistic growth occurs when resources are limited and population size approaches carrying capacity.

  2. 2

    Add for 2 marks

    Example: Bacteria in a fresh nutrient medium may show rapid exponential increase for some time. A deer population in a forest usually follows logistic growth because food, space and predation limit unlimited increase.

  3. 3

    Add for 3 marks

    Population growth depends on births, deaths, immigration and emigration.

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