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A 50-gallon barrel is filled completely with pure water. Salt water with a concentration of 0.3 pounds/gallon is then pumped into the barrel, and the resulting mixture overflows at the same rate. The amount of salt (in pounds) in the barrel at time t (in minutes) is given by Q(t) = 15(1-e) where k> 0 (a) Find k if there are 12.5 pounds of salt in the barrel after 30 minutes. Round your answer to 4 decimal places. (b) What happens to the amount of salt in the barrel ast? Q-Select-

A 50-gallon barrel is filled completely with pure water. Salt water with a concentration of 0.3 pounds/gallon is then pumped into the barrel, and the resulting mixture overflows at the same rate. The amount of salt (in pounds) in the barrel at time t (in minutes) is given by Q(t) = 15(1-e) where k> 0 (a) Find k if there are 12.5 pounds of salt in the barrel after 30 minutes. Round your answer to 4 decimal places. (b) What happens to the amount of salt in the barrel ast? Q-Select-

Advanced Engineering Mathematics
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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A 50-gallon barrel is filled completely with pure water. Salt water with a concentration of 0.3 pounds/gallon is then pumped into the barrel, and the resulting mixture overflows at the same rate. The amount of salt (in pounds) in the barrel at time t (in minutes) is given by Q(t) = 15(1 - e-kt) where k > 0. (a) Find k if there are 12.5 pounds of salt in the barrel after 30 minutes. Round your answer to 4 decimal places. k= (b) What happens to the amount of salt in the barrel as t→ ∞0 ? Q→ ---Select--- ✓
Transcribed Image Text:A 50-gallon barrel is filled completely with pure water. Salt water with a concentration of 0.3 pounds/gallon is then pumped into the barrel, and the resulting mixture overflows at the same rate. The amount of salt (in pounds) in the barrel at time t (in minutes) is given by Q(t) = 15(1 - e-kt) where k > 0. (a) Find k if there are 12.5 pounds of salt in the barrel after 30 minutes. Round your answer to 4 decimal places. k= (b) What happens to the amount of salt in the barrel as t→ ∞0 ? Q→ ---Select--- ✓
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