Part 4 – Logistic Growth & Carrying Capacity

Q1.

The logistic growth equation is:
a) dN/dt = rN
b) dN/dt = rN(K – N)/K
c) dN/dt = K/N
d) dN/dt = B – D

Answer: b) dN/dt = rN(K – N)/K

Explanation:

(a) Exponential growth.
(b) Correct → Logistic model includes carrying capacity (K).
(c) Incorrect equation.
(d) Simplified growth equation.

Q2.

Logistic growth curve is also called:
a) J-shaped curve
b) S-shaped curve
c) U-shaped curve
d) Bell-shaped curve

Answer: b) S-shaped curve

Explanation:

(a) J-shaped → Exponential growth.
(b) Correct → Logistic = S-curve.
(c) U-shaped → Not used in ecology.
(d) Bell-shaped → Age distribution, not growth.

Q3.

Carrying capacity (K) refers to:
a) The maximum growth rate
b) Maximum number of individuals the environment can support
c) Maximum birth rate
d) Mortality rate

Answer: b) Maximum number of individuals the environment can support

Explanation:

(a) Not correct → Growth rate not K.
(b) Correct → K = limit of environment.
(c) Birth rate is not K.
(d) Mortality is not K.

Q4.

The scientist who first proposed the logistic growth model was:
a) Darwin
b) Verhulst
c) Malthus
d) Pearl

Answer: b) Verhulst

Explanation:

(a) Darwin → Evolution, not growth equations.
(b) Correct → Verhulst proposed logistic model (1838).
(c) Malthus → Population theory, exponential.
(d) Pearl → Later contributed, not original.

Q5.

In logistic growth, population grows fastest when:
a) N = 0
b) N = K
c) N = K/2
d) N = 2K

Answer: c) N = K/2

Explanation:

(a) No growth at start.
(b) At K → Growth stops.
(c) Correct → Growth rate max at half K.
(d) N can’t exceed K sustainably.

Q6.

Which phase is absent in logistic growth but present in exponential growth?
a) Lag phase
b) Exponential phase
c) Deceleration phase
d) Stationary phase

Answer: d) Stationary phase

Explanation:

(a) Lag present.
(b) Exponential present.
(c) Deceleration present.
(d) Correct → Exponential growth has no stationary phase, logistic does.

Q7.

Which of the following represents population stabilization?
a) Exponential growth
b) Logistic growth
c) Arithmetic growth
d) Declining growth

Answer: b) Logistic growth

Explanation:

(a) Exponential → Unlimited.
(b) Correct → Logistic includes stabilization at K.
(c) Arithmetic → Linear increase.
(d) Declining → Not stable.

Q8.

Carrying capacity (K) is determined by:
a) Reproductive potential
b) Environmental resistance
c) Mortality rate only
d) Genetic diversity

Answer: b) Environmental resistance

Explanation:

(a) Intrinsic capacity, not K.
(b) Correct → K is set by food, space, predators, competition.
(c) Mortality is only one factor.
(d) Genetic diversity affects adaptation, not K directly.

Q9.

When N approaches K in logistic growth, the value of dN/dt:
a) Becomes zero
b) Becomes maximum
c) Remains constant
d) Becomes negative

Answer: a) Becomes zero

Explanation:
At N = K → dN/dt = rN(K – N)/K = 0.

Q10.

Which population growth is more realistic in nature?
a) Exponential
b) Logistic
c) Linear
d) Constant

Answer: b) Logistic

Explanation:

(a) Exponential → Rare, temporary.
(b) Correct → Logistic considers resource limitation.
(c) Linear → Not natural.
(d) Constant → Not possible.

Q11.

Which stage of logistic growth corresponds to exponential growth?
a) Lag phase
b) Exponential phase
c) Deceleration phase
d) Stationary phase

Answer: b) Exponential phase

Explanation:

(a) Lag = slow start.
(b) Correct → Middle growth is exponential.
(c) Deceleration → Slowing.
(d) Stationary → Growth stops.

Q12.

In logistic growth, environmental resistance is maximum at:
a) Lag phase
b) Exponential phase
c) Stationary phase
d) Initial growth

Answer: c) Stationary phase

Explanation:

(a) Lag = less competition.
(b) Exponential = minimal resistance.
(c) Correct → Near K, resistance max.
(d) Initial → Minimal resistance.

Q13.

Which curve best represents growth of human population in future if resources limit expansion?
a) J-shaped
b) S-shaped
c) Linear
d) Inverted U-shaped

Answer: b) S-shaped

Explanation:
Humans will eventually stabilize near carrying capacity → Logistic (S-curve).

Q14.

At what population size is per capita growth rate (r) maximum in logistic model?
a) N = 0
b) N = K
c) N = K/2
d) N = 2K

Answer: c) N = K/2

Explanation:

At half K, maximum per capita growth.

Q15.

Which of the following is density-dependent regulation?
a) Predation
b) Disease
c) Competition
d) All of the above

Answer: d) All of the above

Explanation:

All these intensify as population nears K.

Q16.

Which is NOT true for logistic growth?
a) Resources are unlimited
b) Carrying capacity exists
c) Growth slows as N nears K
d) Stabilization occurs at K

Answer: a) Resources are unlimited

Explanation:
Unlimited resources → Exponential growth, not logistic.

Q17.

The point at which logistic curve starts bending is called:
a) Inflection point
b) Doubling point
c) Carrying capacity
d) Growth equilibrium

Answer: a) Inflection point

Explanation:
Inflection point = N = K/2, where curve bends.

Q18.

Which species show logistic growth in natural ecosystems?
a) Yeast in fresh medium
b) Reindeer population
c) Invasive weeds
d) Human beings in early history

Answer: b) Reindeer population

Explanation:

(a) Yeast → Exponential initially.
(b) Correct → Reindeer stabilize near K.
(c) Invasives → Initially exponential.
(d) Humans → Historically exponential.

Q19.

What is the carrying capacity of Earth estimated for humans?
a) 2 billion
b) 5 billion
c) 10–12 billion
d) Unlimited

Answer: c) 10–12 billion

Explanation:
Ecologists estimate Earth’s carrying capacity ~10–12 billion.

Q20.

Which factor does NOT determine carrying capacity?
a) Food availability
b) Water supply
c) Climate conditions
d) Genetic code of species

Answer: d) Genetic code of species

Explanation:

Carrying capacity depends on environment, not genome sequence.

Q21.

Population overshoot beyond K may result in:
a) Crash
b) Stabilization
c) Oscillations
d) All of the above

Answer: d) All of the above

Explanation:
Overshoot can lead to temporary crash, oscillations, or stabilization.

Q22.

Logistic growth is mathematically represented by:
a) Nt = N0e^rt
b) dN/dt = rN
c) dN/dt = rN(K – N)/K
d) Nt = N0 + rt

Answer: c) dN/dt = rN(K – N)/K

Explanation:
Correct logistic equation.

Q23.

In logistic model, when N is much smaller than K, growth is almost:
a) Zero
b) Negative
c) Exponential
d) Constant

Answer: c) Exponential

Explanation:
When N ≪ K, (K – N)/K ≈ 1 → reduces to exponential growth.

Q24.

Which term best describes resource limitation controlling population size?
a) Biotic potential
b) Environmental resistance
c) Carrying potential
d) Density independence

Answer: b) Environmental resistance

Explanation:
Environmental resistance = limits of resources and competition.

Q25.

Which growth model is more useful for wildlife management and conservation?
a) Exponential
b) Logistic
c) Linear
d) Arithmetic

Answer: b) Logistic

Explanation:

Exponential → Unrealistic in long term.
Logistic → Considers K, practical for conservation.
Linear/Arithmetic → Not suitable.

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Part 4 – Logistic Growth & Carrying Capacity