A tank initially contains a solution of 14 pounds of salt in 50 gallons of water. Water with 1/5 pound of salt per gallon is added to the tank at 6 gal/min, and the resulting solution leaves at the same rate. Let Q(t) denote the quantity (lbs) of salt at time t (min). (a) Write a differential equation for Q(t). Q' (t) = (b) Find the quantity Q(t) of salt in the tank at time t > 0. (c) Compute the limit. lim Q(t) = t48

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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A tank initially contains a solution of 14 pounds of salt in 50 gallons of water. Water with 1/5 pound of salt
per gallon is added to the tank at 6 gal/min, and the resulting solution leaves at the same rate. Let Q(t)
denote the quantity (lbs) of salt at time t (min).
(a) Write a differential equation for Q(t).
Q' (t) =
(b) Find the quantity Q(t) of salt in the tank at time t > 0.
(c) Compute the limit.
lim Q(t) =
t48
✓
Oll
6
esc
1
@
2
#
3
C
$
4
%
5
&
7
O
8
O
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9
0
Transcribed Image Text:A tank initially contains a solution of 14 pounds of salt in 50 gallons of water. Water with 1/5 pound of salt per gallon is added to the tank at 6 gal/min, and the resulting solution leaves at the same rate. Let Q(t) denote the quantity (lbs) of salt at time t (min). (a) Write a differential equation for Q(t). Q' (t) = (b) Find the quantity Q(t) of salt in the tank at time t > 0. (c) Compute the limit. lim Q(t) = t48 ✓ Oll 6 esc 1 @ 2 # 3 C $ 4 % 5 & 7 O 8 O ( 9 0
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