A coffee shop currently sells 470 lattes a day at $3.50 each. They recently tried raising the by priceby $0.25 a latte, and found that they sold 50 less lattes a day.a) Assume that the number of lattes they sell in a day, N, is linearly related to the sale price, 'p' (indollars). Find an equation for N as a function of p.N(p) =b) Revenue (the amount of money the store brings in before costs) can be found by multiplying thecost per cup times the number of cups sold. Again using p as the sales price, use your equationfrom above to write an equation for the revenue, R as a function of p.Rip) =c) The store wants to maximize their revenue (make as much money as possible). Find the value ofè that will maximize the revenue (round to the nearest cent).which will give a maximum revenue of S

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Answered: A coffee shop currently sells 470…

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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Problem: After being built, a car must be painted. The revenue, R, in dollars, when x cars are painted can be modelled by the function R(x) = 1000x – 0.01x2. a) Determine the average rate of change of revenue when painting 20 to 50 cars. b) Estimate the instantaneous rate of change of revenue after painting 50 cars. c) Interpret the results found in parts a) and b).
According to the Association of American Railroads, Class I freight railroads are the line-haul freight railroads with 2006 operating revenue in excess of $346.8 million. Let F = F(t) denote the freight revenue in billions of dollars of Class I railroads in year t. In 2005, Class I railroads had a freight revenue of $44.5 billion. In 2007, the revenue was $52.9 billion. Calculate the average rate of change per year in F from 2005 to 2007. billion dollars per year Explain in practical terms what this means. O This is the value, in billions of dollars, by which the freight revenue for Class I railroads decreased, on average, over this two-year period. O This is the value, in billions of dollars, describing the average difference in freight revenue for Class I and Class II railroads. O This is the number of years, on average, it takes for the freight revenue for Class I railroads to decrease by 2 billion dollars. This is the number of years, on average, it takes for the freight revenue…
(メ-(S/) sp= Soo=イ Plot the following function
6.) The production of steel by a factory reached P(t) = 500t + 2t² + 20ln (t + 1) tons of steel t weeks after it started its production. Find the rate of change of the steel production of the factory 3 weeks after it started its production. Express the answer in the proper units.
A 100-gal tank initially contains 25% dye solution. A 40% dye solution is allowed to enter at a rate of 10 gal/min and the resulting uniform mixture is removed from the tank at the same rate. a. Derive an expression for the amount of dye in the tank as a function of time. b. Find the time t at which the tank contains 23 % dye solution.
8. The Federal debt held by the public as a percent of the gross domestic product (GDP) is modeled by the function y = 0.00630t3 – 0.289t² + 4.00t + 25.3 where t is the time (in years) since 1980. Find the average public debt as a percent of GDP, from 2000 to 2015.
During Ricardo noticed an ink stain with a diameter of about 3 cm on the front of his teacher’s shirt. He then noticed that there was a pen in the pocket and that the ink blot was continuing to spread across the front of the teacher’s shirt. He estimated that the diameter of the ink blot seemed to be growing by about 0.5 cm every 2 minutes. a) Write an equation for the RADIUS, r, of the ink stain, as a function of time, t. Assume that t = 0 represents the time that Ricardo first noticed the ink stain. b) Write an equation showing the AREA, A, of the ink stain as a function of the time t. (Hint: It might help to first write A as a function of r. ) c) Draw a graph of the function A(t) for 10 minutes. d) At what time is the area of the ink stain about 25 square centimeter? Show how you answer this question. (i.e. ”I found it using desmos” is not sufficient)
1. When you swim underwater, the pressure in your ears depends on the depth at which you are swimming. The formula p=0.43d relates the water pressure p, in pounds per square feet, to a depth of d feet. We can use this linear function to determine the pressure in your ears at a different depths. (a) If your depth is doubled, how did the pressure change? (b) Fill in the blank: i. If the depth is increasing, the pressure is ii. If the depth is decreasing, the pressure is
A 100-gal tank initially contains 25% dye solution. A 40% dye solution is allowed to enter at a rate of 10 gal/min and the resulting uniform mixture is removed from the tank at the same rate.a. Derive an expression for the amount of dye in the tank as a function of time.b. Find the time t at which the tank contains 25% dye solution
A tractor has an initial price of $8000.00 and sells for $1100.00 after 23 years. Assume that the tractor's value depreciates linearly with the passing years. (a) Let V represent the tractor's value in dollars and let t represent the number of years since the tractor was purchased. Write a formula to express the tractor's value as a function of time: V(t) = ... ... (b) Horizontal intercept of the value function V(t): ... Vertical intercept of the value function V(t):
The amount of time it takes to drive somewhere is inversely proportional to the speed at which you drive. The time of a trip is 3 hours when you drive at 60 km/h. a) Determine the equation for the function t(v), which relating the time of the trip ("t", in hours) to the speed (v, in km/h). b) Find the time it would take to complete the above trip if you drove at 90 km/h. c) What speed should you drive at to complete the trip in 75 minutes? 2.
X₁ 2009 2010 2011 2012 2013 2014 2015 2016 (2 N 3₁ 45.3 50.2 51.4 50.2 52.9 54.1 55 57.25 powered by desmos X Y: # of gym memberships (in millions) 58- 56- 54- 52- 50- -48- 46- 44- 42- 4008 (2010, 50.2) 2009 (2009, 45.3) 2010 (2011, 51.4) (2012, 50.2) (2013, 52.9) 2011 x: Year 2012 2013 (2016, 57.25) (2015, 55) (2014, 54.1) 2014 2015 2016

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