Q.146 Botany ⭐ 360° Option Elimination Active

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NEET 2021 Botany Question 146 Solution

Topic: Organisms and Populations · Official NTA Booklet Code M1

Question

In the exponential growth equation Nt=Noert, e represents:

(1)The base of number logarithms
(2)The base of exponential logarithms
(3)The base of natural logarithms
(4)The base of geometric logarithms

✓

Verified Against NTA Final Answer Key

Option (3) : The base of natural logarithms

📚 Organisms and Populations Easy

📋 Given Parameters & Problem Setup

Equation N_t = N_0 e^{rt}

Target Variable Physical/mathematical meaning of the base "e"

⚡

The 30-Second Exam Hall Shortcut: ⚡ Euler's Number "e" = Base of Natural Logarithms (ln)!

⏱️ Save ~10 seconds

In the integrated exponential growth equation $N_t = N_0 e^{rt}$ , $e$ represents Euler's constant ( $e \approx 2.71828$ ), which is the base of natural logarithms ( $\ln$ )! Match Option (3)!

N_t

= Population density at time

t

N_0

= Initial population density at time zero.

r

= Intrinsic rate of natural increase.

e

= Base of natural logarithms (approximately 2.71828).

5 Match Option (3).

🛡️

Why You Can 100% Trust This Shortcut: Canonical NCERT Organisms and Populations on Exponential Growth Formulations.

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Derivation and Parameters of the Exponential Growth Curve

When resources in the habitat are unlimited, the rate of increase of population density is given by the differential equation:

\frac{dN}{dt} = rN

Step 2

Integrated Exponential Equation

Integrating between limits $N_0$ and $N_t$ over time duration $t$ yields the exponential form:

\int_{N_0}^{N_t} \frac{dN}{N} = r \int_0^t dt \implies \ln\left(\frac{N_t}{N_0}\right) = rt \implies \mathbf{N_t = N_0 e^{rt}}

Step 3

Parameter Identification from Canonical NCERT Legend

The NCERT textbook explicitly lists the legend for this formula: - $N_t$ = Population density after time $t$ - $N_0$ = Population density at time zero - $r$ = Intrinsic rate of natural increase - $e$ = The base of natural logarithms ( $2.71828$ )

⭐

360° Option Elimination Engine Key Feature

Diagnose every choice: Know exactly why the right option works and why distractors fail.

4-Option Deep Scan

1 1

✗ Incorrect

Verdict & Scientific Reason:

Fictitious mathematical phrasing; common logarithms use base 10.

⚠️

Student Fallacy (Why candidates pick this trap): Confusing standard common logarithms with base e.

2 2

✗ Incorrect

Verdict & Scientific Reason:

Incorrect non-standard mathematical terminology.

⚠️

Student Fallacy (Why candidates pick this trap): Assuming exponential equation implies "exponential logarithms".

3 3

✓ 100% Correct

Verdict & Scientific Reason:

Exact mathematical and textbook definition of constant e ( $e = 2.71828$ , base of Napierian/natural logarithm ln).

💡

Why this is airtight: None. Textbook definition.

4 4

✗ Incorrect

Verdict & Scientific Reason:

Fabricated distractor term.

⚠️

Student Fallacy (Why candidates pick this trap): Conflating geometric growth with a non-existent "geometric logarithm".

⚠️

NTA Trap Alert: Common vs Natural Logarithm Confusion

Students who remember logarithms recall base 10 (common logs) rather than base e (natural logs, ln).

🛡️ How to avoid the -1 mark: Remember:

e

is Euler's constant

\implies

base of NATURAL logarithms.

📖

Core NEET Syllabus Standard

NEET / NCERT Biology · Organisms and Populations Standard Benchmark

Core Scientific Principle Tested:

"The integral form of exponential growth is Nt = N0 e^(rt), where e is the base of natural logarithms (2.71828)."

Syllabus Focus: Populations: Population Growth Models

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2021 Botany Question 146 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Euler's Number "e" = Base of Natural Logarithms (ln)!

Step-by-Step Rigorous Workflow & Mathematical Proof

Derivation and Parameters of the Exponential Growth Curve

Integrated Exponential Equation

Parameter Identification from Canonical NCERT Legend

360° Option Elimination Engine Key Feature

NTA Trap Alert: Common vs Natural Logarithm Confusion

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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