The 30-Second Exam Hall Shortcut: ⚡ Zero Population Growth (ZPG) Rule
b = d ⟹ r = 0 ⟹ Population Size NEVER CHANGES!
Step-by-Step Rigorous Workflow & Mathematical Proof
Calculate Intrinsic Rate of Natural Increase (r)
In population ecology, the intrinsic rate of natural increase (r) is determined by subtracting the per capita death rate (d) from the per capita birth rate (b).
- • r is the vital statistic measuring inherent capacity of a population to grow.
Apply Exponential Growth Equation
The population size after t time periods is given by the integral form of exponential growth. When r = 0, e^(rt) = e^0 = 1, meaning the population remains completely stationary.
- • Stationary population exhibiting Zero Population Growth (ZPG).
360° Option Elimination Engine Key Feature
Diagnose every choice: Know exactly why the right option works and why distractors fail.
Incorrect. Population would only double if r > 0.
Incorrect. Reduction would require death rate to exceed birth rate (d > b).
100% mathematically and ecologically exact. Since b = d, r = 0, and population remains constant at 10 million.
Incorrect. The population is not going extinct.
NTA Trap Alert: Growth Rate Zero vs. Population Zero Confusion
Careless students sometimes confuse the rate of growth (dN/dt = 0) with the population size (N = 0). A growth rate of zero means size remains CONSTANT.
Core NEET Syllabus Standard
"dN/dt = (b - d) × N; when b = d, dN/dt = 0 and population size remains constant."