Part 3 – Population Growth Models: Exponential Growth

Q1.

The exponential 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: a) dN/dt = rN

Explanation:

(a) Correct → Exponential growth rate depends only on r and N.
(b) Logistic growth.
(c) Wrong → No such formula.
(d) B – D → Simplified growth, not full exponential equation.

Q2.

In exponential growth, “r” represents:
a) Carrying capacity
b) Intrinsic rate of natural increase
c) Immigration rate
d) Mortality rate

Answer: b) Intrinsic rate of natural increase

Explanation:

(a) K → Logistic growth.
(b) Correct → r = intrinsic capacity to grow.
(c) Immigration → External factor.
(d) Mortality → One component, not r.

Q3.

If a population of 1000 increases to 1200 in one year, what is ΔN?
a) 200
b) 1000
c) 1200
d) 2200

Answer: a) 200

Explanation:
ΔN = N₂ – N₁ = 1200 – 1000 = 200.

Q4.

Which type of growth curve is represented by exponential growth?
a) J-shaped curve
b) S-shaped curve
c) Linear curve
d) Bell-shaped curve

Answer: a) J-shaped curve

Explanation:

(a) Correct → Exponential growth forms a J-curve.
(b) Logistic = S-curve.
(c) Linear = straight line.
(d) Bell = age distribution.

Q5.

Which of the following is NOT assumed in exponential growth?
a) Unlimited resources
b) No environmental resistance
c) Carrying capacity present
d) Constant birth and death rates

Answer: c) Carrying capacity present

Explanation:

(a) Assumed.
(b) Assumed.
(c) Correct → No carrying capacity considered in exponential growth.
(d) Assumed.

Q6.

The time taken for a population to double in size is called:
a) Half-life
b) Doubling time
c) Generation time
d) Carrying capacity

Answer: b) Doubling time

Explanation:

(a) Half-life → Radioactivity.
(b) Correct → Doubling time = time to double population.
(c) Generation time → Time between two generations.
(d) Carrying capacity → Environmental limit.

Q7.

The formula for doubling time (Td) is:
a) Td = ln(2)/r
b) Td = r/ln(2)
c) Td = N/r
d) Td = 2r

Answer: a) Td = ln(2)/r

Explanation:

(a) Correct → Doubling time formula.
(b) Wrong reciprocal.
(c) Incorrect.
(d) Incorrect.

Q8.

If r = 0.05 per year, what is doubling time (approx)?
a) 7 years
b) 14 years
c) 35 years
d) 70 years

Answer: d) 70 years

Explanation:
Td = 0.693 / 0.01 ≈ 69.3 years → ~70 years.

Q9.

Exponential growth is also called:
a) Geometric growth
b) Arithmetic growth
c) Logistic growth
d) Balanced growth

Answer: a) Geometric growth

Explanation:

(a) Correct → Exponential = geometric progression.
(b) Arithmetic = linear.
(c) Logistic = S-shaped.
(d) Balanced growth = vague.

Q10.

If r > 0, the population will:
a) Decline
b) Remain stable
c) Increase
d) Crash

Answer: c) Increase

Explanation:

(a) r < 0.
(b) r = 0.
(c) Correct.
(d) Only after overshoot in logistic, not exponential.

Q11.

Exponential growth can be sustained only:
a) In nature
b) In laboratories
c) For short periods under natural conditions
d) For indefinite periods

Answer: c) For short periods under natural conditions

Explanation:

(a) Nature limits resources.
(b) Labs also limited.
(c) Correct → Short bursts possible.
(d) Not indefinite.

Q12.

The slope of exponential growth curve keeps:
a) Decreasing
b) Increasing continuously
c) Constant
d) Negative

Answer: b) Increasing continuously

Explanation:

(a) No.
(b) Correct → Growth accelerates continuously.
(c) Not constant.
(d) Not negative.

Q13.

Which of the following organisms often shows exponential growth in nature?
a) Humans
b) Houseflies
c) Yeast in fresh medium
d) All of the above

Answer: d) All of the above

Explanation:

(a) Humans → Historically exponential.
(b) Houseflies → Explosive growth under food abundance.
(c) Yeast → Shows J-curve in culture.
(d) Correct.

Q14.

Carrying capacity is not included in:
a) Logistic growth
b) Exponential growth
c) Both
d) None

Answer: b) Exponential growth

Explanation:

(a) Logistic → Includes K.
(b) Correct → Exponential ignores K.
(c) Not both.
(d) Not true.

Q15.

Which mathematical model was proposed first for population growth?
a) Logistic model
b) Exponential model
c) Verhulst-Pearl model
d) Lotka-Volterra model

Answer: b) Exponential model

Explanation:

(a) Logistic → Later.
(b) Correct → First proposed growth model.
(c) Verhulst logistic.
(d) Lotka-Volterra → Predator-prey, later.

Q16.

In exponential growth, population at time t is given by:
a) Nt = N0 e^rt
b) Nt = N0 + rt
c) Nt = rN0/K
d) Nt = K – N0

Answer: a) Nt = N0 e^rt

Explanation:

(a) Correct formula.
(b) Linear model.
(c) Wrong.
(d) Wrong.

Q17.

If a bacterium divides every 20 minutes, how many will be present after 2 hours starting with one?
a) 8
b) 16
c) 64
d) 64

Answer: d) 64

Explanation:
2 hours = 120 min → 120/20 = 6 divisions.
Population = 2^6 = 64.

Q18.

Exponential growth is most realistic for:
a) Bacteria in fresh medium
b) Stable human populations
c) Elephants in wild
d) Trees in a forest

Answer: a) Bacteria in fresh medium

Explanation:

(a) Correct → Shows J-curve initially.
(b) Humans → Logistic in future.
(c) Elephants → Slow growth.
(d) Trees → Logistic growth.

Q19.

Which factor usually stops exponential growth in nature?
a) Predation
b) Limited resources
c) Disease
d) All of the above

Answer: d) All of the above

Explanation:

(a) Predators limit growth.
(b) Food, water, space limit.
(c) Diseases check numbers.
(d) Correct.

Q20.

What is the main difference between exponential and logistic growth curves?
a) Logistic has carrying capacity
b) Exponential is J-shaped
c) Logistic is S-shaped
d) All of the above

Answer: d) All of the above

Explanation:
All points are true.

Q21.

Which stage of population growth curve is absent 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 absent in exponential.
(d) Correct → Stationary absent.

Q22.

Human population growth in the last 200 years has been:
a) Logistic
b) Linear
c) Exponential
d) Declining

Answer: c) Exponential

Explanation:

(a) Logistic → Not yet.
(b) Linear → Too simplistic.
(c) Correct → J-shaped historically.
(d) Declining → Not globally.

Q23.

Exponential growth is possible only when:
a) Environment resistance is zero
b) Resources are unlimited
c) Birth rate is higher than death rate
d) All of the above

Answer: d) All of the above

Explanation:
All are essential conditions for exponential growth.

Q24.

Which term describes rapid population increase seen in invasive species in a new habitat?
a) Logistic growth
b) Exponential growth
c) Declining growth
d) Linear growth

Answer: b) Exponential growth

Explanation:
Invasive species often expand exponentially.

Q25.

What is the main limitation of exponential growth model?
a) Assumes unlimited resources
b) Does not consider carrying capacity
c) Unrealistic in long term
d) All of the above

Answer: d) All of the above

Explanation:
All limitations are true, making it an idealized model.

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Part 3 – Population Growth Models: Exponential Growth