The infrastructure needs of a region (for example, thenumber of miles of electrical cable, the number of milesof roads, the number of gas stations) depend on its pop-ulation. Cities enjoy economies of scale.² For example,the number of gas stations is proportional to the popu-lation raised to the power of 0.77.(a) Write a formula for the number, N, of gas stationsin a city as a function of the population, P, of thecity.(b) If city A is 10 times bigger than city B, how dotheir number of gas stations compare?(c) Which is expected to have more gas stations perperson, a town of 10,000 people or a city of500,000 people?

The number of gas stations is proportional to the population raised to power of 0.77.a) Writes a…

Answered: The infrastructure needs of a region…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Computer-Aided Drawing PERFORMANC TAS A house designer uses computer-aided drawings to illustrate new houses. She likes to show her drawings to clients on a large screen. She often uses the zoom-in function to enlarge the drawings so that clients can see certain features better. Each click of the zoom-in button results in a 10 percent increase in the size of a drawing. (a) On a certain drawing of a house, the width of the front door is 3 inches on screen, using the default settings. Make a table of values to show the width of the door on screen after each of the first four clicks of the zoom-in button. These values should be accurate to the thousandths place, (b) Write an algebraic rule for the function that will give the display size of the door for any number of clicks.
A certain city's power company charges their residents for electricity usage on a daily basis. There is a basic charge of 11.57 cents. For each day the first 10 kWh cost 4.81 cents per kWh and any additional kWhs are 9.69 per kWh. (A kWh, or kilowatt-hour, is a unit of energy.) (a) Complete the following table using the information provided above. kWhkWh 0 5 10 15 20 cost (dollars)cost (dollars) kWhkWh 25 30 35 40 cost (dollars)cost (dollars) (b) We can define a piecewise function f(x)f(x) where xx is the kWh used in a day and f(x)f(x) is the cost, in dollars. This function would have the form f(x)={g(x)h(x)ififx∈Ax∈Bf(x)={g(x)ifx∈Ah(x)ifx∈B What functions g(x)g(x) and h(x)h(x) make up the piecewise function f(x)f(x)? g(x)=g(x)= for A = h(x)=h(x)= for B = Hint: A and B are intervals. If an interval uses ±∞±∞ write inf or -inf . (c) Using the above function, what is the cost of 26 kWh? dollars. (d) For 3 dollars, what is the maximum kWh usage for one…
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