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Suppose the wholesale price of a certain brand of medium-sized eggs p (in dollars/carton) is related to the weekly supply x (in thousands of cartons) by the following equation. 625p² – x² =100 If 24000 cartons of eggs are available at the beginning of a certain week and the price is falling at the rate of 7¢/carton/week, at what rate is the supply changing? 1. Explain difference between implicit and explicit differentiation can give an example for each one. 2. Why is this problem considered a related-rates problem? 3. Find value of p when x = 24 by solving the supply equation for p when x= 24 4. Differentiate implicitly the given equation with respect to time. . You dx

Suppose the wholesale price of a certain brand of medium-sized eggs p (in dollars/carton) is related to the weekly supply x (in thousands of cartons) by the following equation. 625p² – x² =100 If 24000 cartons of eggs are available at the beginning of a certain week and the price is falling at the rate of 7¢/carton/week, at what rate is the supply changing? 1. Explain difference between implicit and explicit differentiation can give an example for each one. 2. Why is this problem considered a related-rates problem? 3. Find value of p when x = 24 by solving the supply equation for p when x= 24 4. Differentiate implicitly the given equation with respect to time. . You dx

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter3: Linear And Nonlinear Functions
Section: Chapter Questions
Problem 26MCQ
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Suppose the wholesale price of a certain brand of medium-sized eggs p (in dollars/carton) is related to the weekly supply x (in thousands of cartons) by the following equation. 625p² – x² =100 If 24000 cartons of eggs are available at the beginning of a certain week and the price is falling at the rate of 7¢/carton/week, at what rate is the supply changing? . You 1. Explain difference between implicit and explicit differentiation can give an example for each one. 2. Why is this problem considered a related-rates problem? 3. Find value of p when x = 24 by solving the supply equation for p when x= 24 4. Differentiate implicitly the given equation with respect to time. 5. Substitute given information and p in answer from (3) and solve for . dt 6. Is the supply rising or falling? 7. What rate is the supply rising or falling? (Round your answer to the nearest whole number.)
Transcribed Image Text:Suppose the wholesale price of a certain brand of medium-sized eggs p (in dollars/carton) is related to the weekly supply x (in thousands of cartons) by the following equation. 625p² – x² =100 If 24000 cartons of eggs are available at the beginning of a certain week and the price is falling at the rate of 7¢/carton/week, at what rate is the supply changing? . You 1. Explain difference between implicit and explicit differentiation can give an example for each one. 2. Why is this problem considered a related-rates problem? 3. Find value of p when x = 24 by solving the supply equation for p when x= 24 4. Differentiate implicitly the given equation with respect to time. 5. Substitute given information and p in answer from (3) and solve for . dt 6. Is the supply rising or falling? 7. What rate is the supply rising or falling? (Round your answer to the nearest whole number.)
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