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

Using Eq. \(1.5\) and showing work, what annual growth rate, in percent, leads to the mathematically convenient factor-of-ten growth every century?

In a classic story, a king is asked to offer a payment as follows: place one grain of rice on one square of a chess board ( 64 squares), then two on the next square, four on the next, 8 on the next, and double the previous on each subsequent square. The king agrees, not comprehending exponential growth. But the final number (adding all the grains) is one less than \(2^{64}\). How many grains is this?

In the spirit of outlandish extrapolations, if we carry forward a \(2.3 \%\) growth rate \((10 \times\) per century \()\), how long would it take to go from our current \(18 \mathrm{TW}\left(18 \times 10^{12} \mathrm{~W}\right)\) consumption to annihilating an entire earth-mass planet every year, converting its mass into pure energy using \(E=m c^{2} ?\) Things to know: Earth's mass is \(6 \times 10^{24} \mathrm{~kg} ; c=3 \times 10^{8} \mathrm{~m} / \mathrm{s} ;\) the result is in Joules, and one Watt is one Joule per second.

Your skin temperature is about \(308 \mathrm{~K}\), and the walls in a typical room are about \(295 \mathrm{~K}\). If you have about \(1 \mathrm{~m}^{2}\) of outward-facing surface area, how much power do you radiate as infrared radiation, in Watts? Compare this to the typical metabolic rate of \(100 \mathrm{~W}\).

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)?
See all solutions

Recommended explanations on Environmental Science Textbooks

Physical Environment

Read Explanation

Energy Resources

Read Explanation

Ecology Research

Read Explanation

Pollution

Read Explanation

Environmental Research

Read Explanation

Ecological Conservation

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