Answered: An article† in The New York Times…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.7: Applications

Problem 14EQ

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An article† in The New York Times states, "The number of gas stations [in a city] grows only in proportion to the 0.77 power of population." This means that the approximate number G of gas stations in a city is a power function of the population N, and the power is

k = 0.77.

That is,

G = cN^0.77,

where c is some (as yet) unknown constant. We measure N in millions.

(a)

If one city is twice as large as another, how do the numbers of gas stations compare? (Round your answer to two decimal places)

If one city is twice as large as another, it has about times as many gas stations.

(b)

The population of City A, is 2.3 million and there are 1238 gas stations in City A. Use this information to find the value of c. (Round your answer to two decimal places.)

c =

(c)

City B has a population of about 3.5 million. Using the value of c that you found in part (b), estimate the number of gas stations in City B. Round your answer to the nearest whole number.

gas stations

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