The demand for a 12-ounce bottle of sparkling water is given in the table. Demand Schedule for Sparkling Water in 12-ounce Bottles Price (dollars per bottle) Demand (million bottles) 2.29 25 2.69 9 3.09 3 3.49 2 3.89 1 4.29 0.5 (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 places. Be sure you use the correct input variable p.) D(p) = 1520.42 0.15^p Does the model indicate a price above which consumers will purchase no bottles of water? The model is exponential and does not cross the 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 $3.11? (Round your answer to two decimal places.) 4.16 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.) $ million (d) Calculate consumer surplus when the market price is $3.11. (Round your answer to two decimal places.) $ 2.20 million
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(a) To write the exponential model that gives demand in million bottles as a function of price per bottle p, we can use the formula: D(p) = a * e^(b*p) where D(p) is the demand in million bottles, p is the price per bottle, and a and b are constants that we need Show more…
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