Understanding Population Growth Models
Quick Answer: Population growth models describe how a population size changes over time. Exponential growth assumes unlimited resources, while logistic growth includes carrying capacity.
Key Formulas
Exponential: Nt = N0ert. Logistic: Nt = K / [1 + ((K-N0)/N0)e-rt]. Here N0 = initial population, r = intrinsic growth rate, t = time, K = carrying capacity.
Solved Examples
N0=100, r=0.5/hr, t=5h
Nt=100e2.5
=100*12.18=1218
Rapid growth
N0=10, r=0.3, K=1000, t=20
Nt≈ 1000
Approaches carrying capacity
td = ln2/r
r=0.1 gives td≈6.93
Inverse relation
FAQs
Carrying capacity is the maximum population size that an environment can sustain indefinitely, given available resources like food, water, and space.
r-selected species have high growth rates and produce many offspring (e.g., bacteria). K-selected species live near carrying capacity with fewer offspring but more parental care (e.g., elephants).
Overshoot leads to resource depletion, increased mortality, and a population crash. The population may oscillate around K or decline sharply.