Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Problem 1

Verify the claim in the text that the town of 100 residents in 1900 reaches approximately 100,000 in the year 2000 if the doubling time is 10 years.

Short Answer

Expert verified
Question: In a town, the population was 100 in the year 1900, and its doubling time was 10 years. Verify the claim that the population would reach approximately 100,000 after 100 years. Answer: The claim is true as the population reaches approximately 102,400 in the year 2000.

Step by step solution

01

Identify given values

The initial population in 1900 (P0) is 100 residents, the doubling time is 10 years, and we need to find the population after 100 years (t = 100).
02

Exponential growth formula

The formula for exponential growth is P(t) = P0 * 2^(t/d), where P(t) is the population at time t, P0 is the initial population, t is the number of years, and d is the doubling time.
03

Substitute given values into the formula

P(t) = 100 * 2^(100/10). Here, P0 = 100, t = 100, and d = 10.
04

Calculate the population in the year 2000

P(t) = 100 * 2^(100/10) = 100 * 2^10 = 100 * 1024 = 102,400. The population approximately reaches 100,000 in the year 2000. The claim is verified.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

In the more dramatic bacteria-jar scenario in which doubling happens every minute and reaches single-jar capacity at midnight, at what time will the colony have to cease expansion if an explorer finds three more equivalent jars in which they are allowed to expand without interruption/delay?

A more dramatic, if entirely unrealistic, version of the bacteria-jar story is having the population double every minute. Again, we start the jar with the right amount of bacteria so that the jar will be full 24 hours later, at midnight. At what time is the jar half full now?

If a one-liter jar holds \(10^{16}\) bacteria, how many bacteria would we start in the jar so that the jar reaches full capacity after 24 hours if we increase the doubling time to a more modest/realistic 30 minutes?

If a human body having an outward surface area of \(1 \mathrm{~m}^{2}\) continued to put out \(100 \mathrm{~W}\) of metabolic power in the form of infrared radiation in the cold of space (naked; no sun), what would the equilibrium temperature be? Would this be comfortable (put in context)?

In extrapolating a \(2.3 \%\) growth rate in energy, we came to the absurd conclusion that we consume all the light from all the stars in the Milky Way galaxy within 2,500 years. How much longer would it take to energetically conquer 100 more "nearby" galaxies, assuming they are identical to our own?
See all solutions

Recommended explanations on Environmental Science Textbooks

Energy Resources

Read Explanation

Sustainability

Read Explanation

Environmental Policy

Read Explanation

Environmental Research

Read Explanation

Living Environment

Read Explanation

Physical Environment

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.

Sign-up for free