Describe the exponential and logistic models of population growth with their equations and growth curves. Which is more realistic?

1. 1 · Open with the idea. Growth depends on resources: unlimited resources give exponential growth; limited resources give logistic growth.
2. 2 · Explain exponential growth.
   • dN/dt = (b − d)N = rN, where r is the intrinsic rate of natural increase.
   • Integral form: Nₜ = N₀ eʳᵗ.
   • Gives a J-shaped curve.
3. 3 · Explain logistic growth.
   • Limited resources; carrying capacity K.
   • dN/dt = rN (K − N)/K.
   • Lag, acceleration, deceleration and asymptote: an S-shaped curve.
4. 4 · Draw both curves on one graph. [Graph: N on the y-axis, time on the x-axis; J-curve labelled exponential; S-curve labelled logistic; dashed line labelled K]
5. 5 · Say which is realistic. Logistic, because resources for growth are finite and become limiting sooner or later.
6. 6 · Link to real life. Resources are finite, so many governments, including India's, have brought in measures to limit human population growth.
7. 7 · Close in one line. So the carrying capacity, set by resources, decides where a population stops growing.

Scoring tip: Write both equations and define r and K. One graph with both curves and a labelled K line saves time.