Problem 51 - Objective Biology for NEET

Question

In expression of exponential growth ' \(\mathrm{r}\) ' is referred to as (a) Growth rate (b) Efficiency index (c) Both (a) and (b) (d) Time of growth

Step-by-Step Solution

Answer

The variable '\(r\)' in the expression of exponential growth refers to (a) Growth rate.

Step 1: Understand the Terminology

In the context of exponential growth, '\(r\)' stands for the rate of growth. This is the proportion by which a population increases or decreases for each unit of time.

Step 2: Choose the Correct Option

From the given options, it's clear that option (a) Growth rate correctly defines the term '\(r\)' in the context of exponential growth.

Key Concepts

Rate of Growth

In biology, understanding the rate of growth is crucial when examining how populations develop over time. The rate of growth, often denoted by the letter '\(r\)', represents the speed at which a population expands or contracts in a given period. Envision small populations like bacteria that multiply incredibly fast. The rapid increase is due to a high rate of growth. You can think of it as the pace at which new individuals are added.
This rate is an essential part of the exponential growth model, which explains how populations grow by increasing more and more each interval, building on the amount already there. This rate is continuous and does not change unless external conditions do. Understanding this helps in gauging how other factors might influence a population’s rise or decline.

• The higher the rate of growth, the faster the population increases.
• A constant rate leads to exponential growth, meaning the population doubles at regular intervals.
• It's important in predicting future population sizes and in planning for ecological impacts.

Population Increase

Population increase is the result of a positive rate of growth. As populations expand, understanding the intricacies of what causes such growth becomes essential. This is typically due to births and immigration rates exceeding deaths and emigration.
In nature, populations tend to grow when resources are abundant. For example, a group of rabbits in a field with plenty of grass and no predators can grow rapidly.
This increase is often modeled by the exponential growth formula, which helps predict how many individuals will be present in the future if the current conditions persist.

• An increasing population can strain resources, affecting food availability.
• Climate changes and habitat destruction can alter the rate of population growth.
• Understanding population increase is vital for conservation efforts and resource management.

Growth Rate Definition

The growth rate is a fundamental concept that describes how fast a population is increasing or decreasing over time. It is usually expressed as a percentage or fractional increase per time unit, providing a clear measure of population change.
In scientific terms, the growth rate can be mathematically illustrated by the equation \(P(t) = P_0 e^{rt}\), where:

• \(P(t)\) is the future population after time \(t\).
• \(P_0\) is the initial population size.
• \(r\) is the rate of growth.
• \(e\) is the base of the natural logarithm.

This equation highlights how the initial size and rate of growth contribute to future changes. A positive growth rate indicates a burgeoning population, whereas a negative growth rate signals a decline. Familiarizing yourself with this definition helps in forecasting various biological processes, economic models, and even in policy-making for sustainable development in communities.