Question

Zipf's Law, developed by George Zipf in 1949, states that in a given country, the population of a city is inversely proportional to the city's rank by size in the country.116 Assuming Zipf's Law:
(a)
Write a formula for the population, P, of a city as a function of its rank, R.
(b)
If the constant of proportionality k is 300,000, what is the approximate population of the largest city (rank 1)? The second largest city (rank 2)? The third largest city?
(c)
Answer the questions of part (b) if k = 6 million.
(d)
Interpret the meaning of the constant of proportionality k in this context.

Expert Solution

Want to see the full answer?

Check out a sample Q&A here
Blurred answer
Students who’ve seen this question also like:
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN: 9781133382119
Author: Swokowski
Publisher: Cengage
Not helpful? See similar books
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Polynomial And Rational Functions. 28E
marketing sidebar icon
Want to see this answer and more?
Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*
*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.

Related Calculus Q&A

Find answers to questions asked by students like you.

Q: A certain radioactive material is known to decay at a rate proportional to the amount present.…

A: Here, initial mass =50 mg rate is proportional to the amount.m=50e-0.053t dmdtαm

Q: 2. Initially, there are 500 strands of bacteria in a culture. If the growth rate of the population…

A: Click to see the answer

Q: When the annual rate of inflation averages 5% over the next 10 years, the approximate cost C of…

A: Consider the approximation cost of goods. Ct=p1.05t Rate of change of C=dCdt. So, Differentiate the…

Q: Prove that if y = Yoe, where yo and k are constants, then dyldt = ky. (This says that for…

A: Click to see the answer

Q: A park ranger is searching for bears in a region of the park where on average there are 12 bears per…

A: Introduction: It is given that there are 12 bears per square mile of the park. Further, the number…

Q: ydrocodone bitartrate is used as a cough suppressant. After the drug is fully absorbed, the quantity…

A: “Since you have posted a question with multiple sub-parts, we will solve  three sub-parts for you.…

Q: If a population of buffalo are becoming extinct. Assume that 150 years ago there were 100,000…

A: This question is about application of differential equation

Q: 12. If a substance decomposes at a rate proportional to the amount of the substance present, and the…

A: Click to see the answer

Q: (a) In a certain culture of bacteria the rate of increase is proportional to the number present. (i)…

A: Click to see the answer

Q: Q No. 2: Five people in a community with stable population of 5000 people got infected with a…

A: Given: Total population=5000   Let Infected people=pNon-infected people=5000-p……1   and, At time…

Q: A certain radioactive material is known to decay at a rate proportional to the amount present.…

A: Given that:   Initial amount = 50 mg and after two hours the material is 10% less of original…

Q: A certain radioactive material is known to decay at a rate proportional to the amount present.…

A: Let,Decay rate = r = -dAdt                        negative because it's decaying/decreasingwhere, r…

Q: 9. The rate at which the value, V, of a painting changest years after it is completed is given by…

A: Image is attached.

Q: According to Stevens’ Law in psychology, the perceived magnitude of a stimulus is…

A: Click to see the answer

Q: 6. If one earthquake has a magnitude of 5 on the Richter scale and a second earthquake has a…

A: If one earthquake has a magnitude of 5 on the Richter scale and a second earthquake has a magnitude…

Q: 3) An empty can of room freshener that has a volume of 350 mL, contains gas at a pressure of 360 kPa…

A: I am attaching image so that you understand each and every step.

Q: 1. For a substance D, the time rate of conversion is proportional to the square root of the amount x…

A: Click to see the answer

Q: Solve the following: 1. In a certain culture of bacteria, the rate of increases is proportional to…

A: Let the number of bacteria present be x, then the rate of increase is given by x'(t). According to…

Q: By natural increase, a city whose population is 40,000 will double in 50 yrs. There is a net…

A: This question is related to population growth, We will solve it using given information.

Q: (a) In a certain culture of bacteria the rate of increase is proportional to the number present. (i)…

A: Click to see the answer

Q: If the growth rate of bacteria in a culture medium is directly proportional Question 3. to the…

A: Growth rate of Bacteria In culture: Growth of bacteria In culture is defined as an increase in the…

Q: 2. For a substance D, the time rate of conversion is proportional to the square root of the amount x…

A: Given For a substance D, time rate of conversion is proportional to the square root of the amount x…

Q: e population of a certain country is known to increase at a rate proportional to e number of people…

A: Topic:- population growth exponential function

Q: Consider a bacteria culture in which the rate of growth of the population of bacteria is…

A: Click to see the answer

Q: The rate of growth of a bacteria population is proportional to the number of bacteria present. The…

A: Please see the answer below

Q: As a result of COVID-19, some students attended less than H/2 hours of lectures before the college…

A: Consider the provided question, We have to find the average in the class,

Q: Five rodents in a population of 500 are infected with a new strain of corona virus to test a theory…

A: Click to see the answer

Q: Five rodents in a population of 500 are infected with a new strain of corona virus to test a theory…

A: Click to see the answer

Q: d. . As part of the process in the production of a perfume, a certain substance with water is…

A: Click to see the answer

Q: 12. If a substance decomposes at a rate proportional to the amount of the substance present, and the…

A: Click to see the answer

Q: The growth rate of Escherichia coli, a common bacterium found in the human intestine, is…

A: a: it doubles in every 30 minute and initial population = 10 then we can write the function as:…

Q: A group of survivors on a supply run has returned to their base camp with a population of 2000. Two…

A: Given:  y       = present number of infected people 2000 = total population  y'(t)  = rate of spread…

Q: 12. If a substance decomposes at a rate proportional to the amount of the substance present, and the…

A: Click to see the answer

Q: The growth rate of Escherichia coli, a common bacterium found in the human intestine, is…

A: Given The number of cells doubles every 30 minutes. A) Initial Population =1000 B) Initial…

Q: (a) A kitchen sink has a volume of 15 L. If the drain is closed and the sink is initially empty,…

A: Click to see the answer

Q: 1. If three workers can paint a room in two hours, then about how long does it take four workers to…

A: Click to see the answer

Q: 3. The rate of population grarth of a to the number inhabitent>. If the population of a certain…

A: topic - exponential function

Q: The following table gives for a certain man his height H= H(t) in inches at age t in years A- use…

A: From the table, we have (0, 21.5) and (5, 42.5), Now find the slope passing through two points…

Q: The growth rate of Escherichia coli, a common bacterium found in the human intestine, is…

A: (a) Given: The initial population is 500. The number of cells in a culture doubles approximately…

Q: A population is growing at a rate proportional to its size. After 8 ​years, the population size was…

A: Let consider P(t) be the population at a time t. Let P0 is the initial population at time t = 0. To…

Q: Two substances, A and B, are being converted into a single compound C. In the laboratory it has been…

A: Click to see the answer

Q: 1. When the interest on an investment is compounded continuously, the investment grows at a rate…

A: The change in amount with the rate r is dPdt=rP The amount of investment is 20,000. The amount of…

Q: A teacher makes a cup of coffee. At 13:00 the coffee in the cup has a temperature of 86 Celsius and…

A: Given that the initial temperature of the coffee is 86° Celsius and the air temperature of the room…

Q: A teacher makes a cup of coffee. At 13:00 the coffee in the cup has a temperature of 86 Celsius and…

A: (a) It's given that the rate of cooling coffee is proportional to the difference between coffee…

Q: Prove that the relative rate of change 1/f(x)is negative that of f(x). Give a general formula for…

A: The relative rate of change of a function f(x) is the ratio of its derivative to itself. R(f(x)) =…

Q: The acceleration due to gravity, g, is given by GM p2 where M is the mass of the Earth, r is the…

A: Click to see the answer

Q: Oil is pumped continuously from a well at a rate proportional to the amount of oil left in the well.…

A: Explained below

Q: Oil is pumped continuously from a well at a rate proportional to the amount of oil left in the well.…

A: Click to see the answer

Q: A quantity Q1 grows by 1% every hour. If the initial quantity (at t = 0) is Qo = 30, complet the…

A: Click to see the answer

Q: Using the concept of net rate above, determine a model for a population P(t) if the birth rate is…

A: Given information: The rate at which the population changes is a net rate. The net rate is the…

Knowledge Booster
Calculus
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
  • Algebra & Trigonometry with Analytic Geometry
    Algebra
    ISBN:9781133382119
    Author:Swokowski
    Publisher:Cengage
    Functions and Change: A Modeling Approach to Coll...
    Algebra
    ISBN:9781337111348
    Author:Bruce Crauder, Benny Evans, Alan Noell
    Publisher:Cengage Learning
    Algebra and Trigonometry (MindTap Course List)
    Algebra
    ISBN:9781305071742
    Author:James Stewart, Lothar Redlin, Saleem Watson
    Publisher:Cengage Learning
  • Algebra & Trigonometry with Analytic Geometry
    Algebra
    ISBN:9781133382119
    Author:Swokowski
    Publisher:Cengage
    Functions and Change: A Modeling Approach to Coll...
    Algebra
    ISBN:9781337111348
    Author:Bruce Crauder, Benny Evans, Alan Noell
    Publisher:Cengage Learning
    Algebra and Trigonometry (MindTap Course List)
    Algebra
    ISBN:9781305071742
    Author:James Stewart, Lothar Redlin, Saleem Watson
    Publisher:Cengage Learning