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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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)
The U.S. population can be modeled by the function y=165.6x¹.345, where y is in thousands and x is the number of years after 1800. (a) What was the population in 1970, according to this model? (b) is the graph of this function concave up or concave down? What does this mean? (c) Use numerical or graphical methods to find when the model estimates the population was 94,150,000. (a) According to the model, the population in 1970 was thousands. (Round to the nearest integer as needed.)
1) Consider a function that relates tax revenues R (in billions of dollars) to the average tax rate (t) such that R = 700t – 1000t2a. What average tax rate(s) is consistent with raising tax revenues equal to $120 billion?b. What average tax rate(s) is consistent with raising tax revenues equal to $122.5 billion?
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
Suppose that a student carrying a flu virus returns to campus and that four days later fifty students have been infected. Determine the number of infected students as a function time. Assume that the virus spreads at a rate that is proportional to both the number of students that have been infected and the number of students that have not been infected. Also assume that the campus population is 5000 students.
A 30-second commercial during Super Bowl XXXVII in 2003 cost advertisers 2.2 million. For the first Super Bowl in 1967, an advertiser could have purchased approximately 26.19 minutes of advertising time for the same amount of money. (a) Assuming that advertising cost is proportional to its length of time, find the cost of advertising, in dollars/second, during the 2003 Super Bowl. cost= dollars/second. (round to nearest cent and do not enter commas) (b) Assuming that advertising cost is proportional to its length of time, find the cost of advertising, in dollars/second, during the 1967 Super Bowl. cost = dollars/second. (round to nearest cent and do not enter commas) (c) How many times more expensive was Super Bowl advertising in 2003 than in 1967? times more expensive (round to nearest whole number)

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