The demand for a 12-ounce bottle of sparkling water is given in the table.Demand Schedule for Sparkling Water in12-ounce BottlesPriceDemand(dollars per bottle)(million bottles)2.29252.699.3.093.4923.8914.290.5(a) Write the function for the exponential model that gives demand in million bottles, as a function of price per bottle p, with data from 2.29 < p< 4.29. (Round all numerical values to two decimal plaBe sure you use the correct input variable p.)D(p) =Does the model indicate a price above which consumers will purchase no bottles of water?The model is exponential and does not crossthe horizontal axis. Therefore there is no price above which consumers will not purchase water.(b) What quantity of water will consumers purchase when the market price is $3.81? (Round your answer to two decimal places.)X million bottles(c) Calculate the amount that consumers willing and able to spend to purchase the quantity found in part (b). (Round your answer to one decimal place.)X million(d) Calculate consumer surplus when the market price is $3.81. (Round your answer to two decimal places.)24millionViewing Saved Work Revert to Last ResponseSubmit Answer6:33W)71°F10/5/2DI%24

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Answered: The demand for a 12-ounce bottle of…

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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The growth rate of the speed of sound in relation to the temperature in degrees Fahrenheit is a linear function. The speed of sound at 0 degrees Fahrenheit is 1052.3 feet per second. For every 1 degree Fahrenheit rise in temperature, the speed of sound increases by 1.1 feet per second. A. Identify the initial value of linear function that gives the speed of sound in terms of temperature. B. A 20 degree Fahrenheit rise in temperature would provide what increase in the speed of sound? C. What would the speed of sound be after a 67 degree Fahrenheit rise in temperature?
An economist tracks the price of a certain item at the beginning of several years and compiles the following table. Year 2013 2014 2015 2016 Price in dollars 265.50 273.47 281.67 290.12 (a) Show that the price is growing as an exponential function. (Let P be the price in dollars and t the time in years since 2013.) Calculate the ratios of new price/old price. (Round your answers to two decimal places.) P1 Ро P2 P1 P3 P2 Does the table show exponential data? o Yes o No (b) Find an exponential model for data. (Round to two deci al places. Let t be the in years since 2013.) OP = 304.21 × 0.83° OP = 260.00 × 1.12" OP = 290.12 × 0.97* OP = 265.50 × 1.03t OP = 93.12 × 1.35° (c) At the beginning of some year, the price will surpass $344. Use the model found in part (b) to determine which year.
An economist tracks the price of a certain item at the beginning of several years and compiles the following table. 2014 2015 273.47 281.67 2016 290.12 2013 Year Price in dollars 265.50 (a) Show that the price is growing as an exponential function. (Let P be the price in dollars and t the time in years since 2013.) Calculate the ratios of new price/old price. (Round your answers to two decimal places.) P₁. Po P2, P1 P2 Does the table show exponential data? Yes No (b) Find an exponential model for the data. (Round the values to two decimal places. Let t be the time in years since 2013.) CP= 304.21 x 0.83t P = 290.12 x 0.97t CP= 260.00 x 1.12t P = 93.12 x 1.35* P = 265.50 x 1.03t (c) At the beginning of some year, the price will surpass $344. Use the model found in part (b) to determine which year.
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A new car costs $27, 000 depreciates to 80% of its value in 2 years. Round all answers to 2 decimal places, where necessary. a. Assume that the depreciation is linear. What is the linear function that models the value of this car t years after purchase? f(t) = Preview b. Assume that the value of the car is given by an exponential function Aekt, where A is the initial price of the car. Find the value of the constant k. Answer exactly. k = Preview c. For the linear model used in part (a), find the value of the car 6 years after the purchase, then do the same for the exponential model used in part (b). Round your answer to 2 decimal places. Linear after 6 years: $ Exponential after 6 years: $
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