A tank contains 100 kg of salt and kg 2000 L of water. Water containing 0.3 of salt enters the tank at the rate 8. The solution is mixed and drains from the tank at L min the rate 4. A(t) is the amount of salt in min the tank at time t measured in kilograms. (a) A(0) = 100 (kg) (b) A differential equation for the amount of salt in the tank is 0.15/6 t,A, A', A", for your variables, not A(t), and move everything to the left hand side.) (c) The integrating factor is 8 (d) A(t) = = 0. (Use

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 16E: Find the general solution for each differential equation. Verify that each solution satisfies the...
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A tank contains 100 kg of salt and
kg
2000 L of water. Water containing 0.3% of
salt enters the tank at the rate 8
L
The
min
solution is mixed and drains from the tank at
L
the rate 4 A(t) is the amount of salt in
the tank at time t measured in kilograms.
min
(a) A(0) = 100
(kg)
.
(b) A differential equation for the amount of
salt in the tank is
0.15/6
t,A, A', A", for your variables, not A(t), and
move everything to the left hand side.)
(c) The integrating factor is
8
(d) A(t) =
4
(kg)
=
0. (Use
(e) Find the concentration of salt in the
solution in the tank as time approaches
infinity. (Assume your tank is large enough to
hold all the solution.)
concentration =
0.15/6
kg
L
Transcribed Image Text:A tank contains 100 kg of salt and kg 2000 L of water. Water containing 0.3% of salt enters the tank at the rate 8 L The min solution is mixed and drains from the tank at L the rate 4 A(t) is the amount of salt in the tank at time t measured in kilograms. min (a) A(0) = 100 (kg) . (b) A differential equation for the amount of salt in the tank is 0.15/6 t,A, A', A", for your variables, not A(t), and move everything to the left hand side.) (c) The integrating factor is 8 (d) A(t) = 4 (kg) = 0. (Use (e) Find the concentration of salt in the solution in the tank as time approaches infinity. (Assume your tank is large enough to hold all the solution.) concentration = 0.15/6 kg L
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ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,