/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 1 What is the difference between a... [FREE SOLUTION] | 魅影直播

魅影直播

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 1

What is the difference between a discrete \((\Delta N / \Delta t)\) and continuous \((\mathrm{d} N / \mathrm{d} t)\) model of population growth? What is the difference between geometric and exponential growth?

Short Answer

Expert verified
Question: Explain the differences between a discrete and continuous model of population growth and the differences between geometric and exponential growth. Answer: A discrete model of population growth involves changes in population at fixed time intervals, with the population increasing by a constant proportion or factor at each interval, known as geometric growth. On the other hand, a continuous model of population growth involves continuous changes in population over time, where the rate of population growth is directly proportional to the population size at any given time, known as exponential growth.

Step by step solution

01

Discrete Model of Population Growth

In a discrete model of population growth, changes in population occur at specific time intervals, for example, per day, per month, or per year. The change in population during each time interval is denoted by \((\Delta N / \Delta t)\), where \(\Delta N\) represents the change in population and \(\Delta t\) represents the time interval.
02

Continuous Model of Population Growth

In a continuous model of population growth, the population changes continuously over time. The rate of change of population with respect to time is given by \(\frac{\mathrm{d} N}{\mathrm{d} t}\), where \(\mathrm{d} N\) represents the infinitesimal change in population and \(\mathrm{d} t\) represents the infinitesimal change in time.
03

Geometric Growth

Geometric growth occurs in a discrete model of population growth. In geometric growth, the population increases by a constant proportion or factor at each time interval. This can be represented by the equation \(N_t = N_0(1 + r)^t\), where \(N_t\) is the population at time \(t\), \(N_0\) is the initial population, and \(r\) is the per capita growth rate.
04

Exponential Growth

Exponential growth occurs in a continuous model of population growth. In exponential growth, the rate at which the population grows is directly proportional to the population size at any given time. This can be represented by the equation \(N_t = N_0e^{rt}\), where \(N_t\) is the population at time \(t\), \(N_0\) is the initial population, \(r\) is the per capita growth rate, and \(e\) is the base of the natural logarithm. In summary, a discrete model of population growth consists of changes in population at fixed time intervals and can be described by geometric growth. In contrast, a continuous model of population growth involves continuous changes in population over time and follows exponential growth.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 魅影直播!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

What is a life table? What is the purpose of constructing such tables?

Why are small populations more susceptible to extinction from demographic stochasticity than larger populations?

Identify two factors that could possibly cause a population to decline to extinction. How might population size influence the impact of these factors?

How can the finite growth multiplier be used to predict future values of population density, \(N(t) ?\)
See all solutions

Recommended explanations on Environmental Science Textbooks

Sustainability

Read Explanation

Geology

Read Explanation

Environmental Policy

Read Explanation

Biological Resources

Read Explanation

Ecology Research

Read Explanation

Energy Resources

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.