(Dungeons & Dragons) A party of adventurers is fighting a poisonous slime monster in a cave. The cave initially contains 1000 ft³ of air, 1% of which is poison gas. The slime gives off vapor from its body at a constant rate of 100 ft³/min, 50% of which is poison gas. Air escapes the cave through cracks in the rocks at the same rate, so that the total volume of air in the cave remains constant. a) Draw a phase line for X(t) = the amount of poison gas in the cave at time t (in ft³), and use this picture to argue that the limiting concentration of poison gas in the cave is 50%. b) The human adventurers will become poisoned and die if the concentration of poison gas in the cave exceeds 10%. How long do they have left to fight before they become poisoned?
(Dungeons & Dragons) A party of adventurers is fighting a poisonous slime monster in a cave. The cave initially contains 1000 ft³ of air, 1% of which is poison gas. The slime gives off vapor from its body at a constant rate of 100 ft³/min, 50% of which is poison gas. Air escapes the cave through cracks in the rocks at the same rate, so that the total volume of air in the cave remains constant. a) Draw a phase line for X(t) = the amount of poison gas in the cave at time t (in ft³), and use this picture to argue that the limiting concentration of poison gas in the cave is 50%. b) The human adventurers will become poisoned and die if the concentration of poison gas in the cave exceeds 10%. How long do they have left to fight before they become poisoned?
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:(Dungeons & Dragons) A party of adventurers is fighting a poisonous slime monster in a cave. The
cave initially contains 1000 ft³ of air, 1% of which is poison gas. The slime gives off vapor from its
body at a constant rate of 100 ft³/min, 50% of which is poison gas. Air escapes the cave through
cracks in the rocks at the same rate, so that the total volume of air in the cave remains constant.
a) Draw a phase line for X(t) = the amount of poison gas in the cave at time t (in ft³), and use this
picture to argue that the limiting concentration of poison gas in the cave is 50%.
b) The human adventurers will become poisoned and die if the concentration of poison gas in the
cave exceeds 10%. How long do they have left to fight before they become poisoned?
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