9. Imagine a medieval world. In this world a Queen wants to poison a King, who has a wine keg with 500 L of his favorite wine. The Queen gives a conspirator a liquid containing 5 g/L of poison, which must be poured slowly into the keg at a rate of 0.5 L/min. The poisoner must also remove the well-stirred mixture at the same rate, so that the keg is not suspiciously full. (a) Find a formula for the amount of poison in the keg at any time, measured from the start of the pouring by the poisoner. (b) A plot is hatched for the King to drink wine from the keg while he is on a hunt, where he will become so addled that his prey will surely kill him. The poisoner must pour for a time T, when the poison in the keg reaches a dangerous concentration of 0.005 g/L. Find T. (c) The Lord High Inquisitor of the Realm never learned about differential equations. Nonetheless, knowing the basic numbers (keg size, poison concentrations, etc.), he can produce an estimate for the time T that the poisoner was at the keg. In fact, his estimate is within 2% of the exact value found in part (b). What is the Lord's estimate? In the context of differential equations, why is it so close to the exact value obtained from the solution?
9. Imagine a medieval world. In this world a Queen wants to poison a King, who has a wine keg with 500 L of his favorite wine. The Queen gives a conspirator a liquid containing 5 g/L of poison, which must be poured slowly into the keg at a rate of 0.5 L/min. The poisoner must also remove the well-stirred mixture at the same rate, so that the keg is not suspiciously full. (a) Find a formula for the amount of poison in the keg at any time, measured from the start of the pouring by the poisoner. (b) A plot is hatched for the King to drink wine from the keg while he is on a hunt, where he will become so addled that his prey will surely kill him. The poisoner must pour for a time T, when the poison in the keg reaches a dangerous concentration of 0.005 g/L. Find T. (c) The Lord High Inquisitor of the Realm never learned about differential equations. Nonetheless, knowing the basic numbers (keg size, poison concentrations, etc.), he can produce an estimate for the time T that the poisoner was at the keg. In fact, his estimate is within 2% of the exact value found in part (b). What is the Lord's estimate? In the context of differential equations, why is it so close to the exact value obtained from the solution?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:9. Imagine a medieval world. In this world a Queen wants to poison a King, who has a wine keg
with 500 L of his favorite wine. The Queen gives a conspirator a liquid containing 5 g/L of poison,
which must be poured slowly into the keg at a rate of 0.5 L/min. The poisoner must also remove
the well-stirred mixture at the same rate, so that the keg is not suspiciously full.
(a) Find a formula for the amount of poison in the keg at any time, measured from the start of the
pouring by the poisoner.
(b) A plot is hatched for the King to drink wine from the keg while he is on a hunt, where he will
become so addled that his prey will surely kill him. The poisoner must pour for a time T, when the
poison in the keg reaches a dangerous concentration of 0.005 g/L. Find T.
(c) The Lord High Inquisitor of the Realm never learned about differential equations. Nonetheless,
knowing the basic numbers (keg size, poison concentrations, etc.), he can produce an estimate for
the time T that the poisoner was at the keg. In fact, his estimate is within 2% of the exact value
found in part (b). What is the Lord's estimate? In the context of differential equations, why is it so
close to the exact value obtained from the solution?
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