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?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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.
625p? – x? =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?
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. 625p? – x? =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?
4. Differentiate implicitly the given equation with respect to time.
dx
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:4. Differentiate implicitly the given equation with respect to time. dx 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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