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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An economist predicts that the buying power B(x) of a dollar x years from now will be given by the formula B(x)=0.8*. How much will today's dollar be worth in 2 years? Round to the nearest cent. O A. $1.74 OB. $0.96 OC. $1.60 OD. $0.64
Under a microscope, Ms. Kapinski studies a culture with bacteria. As the number of hours progresses, Ms. Kapinski sees that the bacteria can be modeled by the function ?(?) = 1290(0.76) ? where b represents the number of bacteria t hours after Ms. Kapinski begins her study. (a) What does the value 0.76 represent in this situation? Be sure to explain. (b) What does the value 1290 represent in this situation? Be sure to explain. (c) The number of bacteria in a second study is modeled by the function ?2 (?) = 1180(1.76) ? . i. What does the value of 1180 represent in this situation? ii. What does the difference of 1290 and 1180 mean between the two studies? iii. What does the difference between 0.76 and 1.76 mean between the two studies?
11) n 2000 the population of Alaska was 626,932 people. By 2010, the population grew to 694,109 people. Alaska has been experiencing exponential growth during this time. A) Write a function to model the population of Alaska with respect to time. B) In what year will the population reach 800,000 people? Solve algebraically.
2. An antique computer valued at $6500 depreciates at the rate of 14% per year (b = 0.86). Equation: Circle one: Linear or Exponential 3. The population of flying squirrels in Madagascar started with 3 and the population doubles each year. Equation: Circle one: Linear or Exponential 4. Penny has a stamp collection of 550 stamps. Penny is feeling generous and gives away7 stamps every week. Circle one: Linear or Exponential Equation: 5. The phone company charges a flat rate of $25 per month. In addition they charge $0.05 for each min of service. Write a function to model the relationship between the number of minutes of service each month. 6. Jenny bought a 2016 Ford F-150 for $25,000 which depreciates at a rate of 4.3% per year (b = 0.957). Write a function to model the relationship between time and value of the car. 7. Brian used the equation y = 3x + 7 that represents the new cucumber plant that he bought for his yard, where x represents the weeks since the cucumber plant was planted…
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The area covered by a marsh, A, starts at 130 acres and drops by a factor of 14 each year for n years. Write a formula for A=f(n).
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…
The Jones bought a new house for $149700. Because of economic growth in the area, the value of their house increased at an average rate of 8% per annum for 5 years. To model this growth, use an exponential function of the form y = a·b^x The value of their house after the 5 years, to the nearest dollar, was options: A) $209 580 B) $161 676 C) $198 754 D) $219 958

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