Question 1: Suppose a tank contains 1000 gal of
water and 300 lbs of salt. What is the
concentration of the salt in the water?
(A) 0.3 lbs/gal
(B) 2 lbs/gal
(C) 3 lbs/gal
(D) None of the above
Question 2: Suppose a tank initially contains
1000 gal of water and 300 lbs of salt, and a
mixture containing 2 lbs of salt per gal of water is
piped in at the rate of 2 gal/min, while the tank
is drained at the same rate. At what rate is the
salt deposited into the tank?
(A) 2 lbs/min
(B) 3 lbs/min
(C) 4 lbs/min
(D) None of the above
Question 3: Suppose a tank initially contains
1000 gal of water and 300 lbs of salt, and a
mixture containing 2 lbs of salt per gal of water is
piped in at the rate of 2 gal/min, while the tank
is drained at the same rate. At what rate is the
salt removed from the tank in terms of S(t) – the
amount of salt in the tank at time t?
2S
(A) 500
.
S
(B) 500
S
(C) 1000
(D) None of the above
Question 4: Suppose a tank initially contains
1000 gal of water and 300 lbs of salt, and a
mixture containing 2 lbs of salt per gal of water is
piped in at the rate of 2 gal/min while the tank is
drained at the same rate. What is the differential
equation describing the change in the amount of
salt in the tank?
3S
(A) S 0 = 4 + 500
.
S
0
(B) S = 4 − 500
3S
(C) S 0 = −4 − 500
(D) None of the above
Question 5: Suppose a tank initially contains
1000 gal of water and 300 lbs of salt and a
mixture containing 2 lbs of salt per gal of water is
piped in at the rate of 2 gal/min while the tank is
drained at the same rate. What is the initial
condition corresponding to this problem?
(A) S 0 (0) = 250
(B) S(0) = 500
(C) S(0) = 300
(D) None of the above
Question 6: Suppose a tank initially contains
1000 gal of water and 300 lbs of salt and a
mixture containing 2 lbs of salt per gal of water is
piped in at the rate of 2 gal/min while the tank is
drained at the same rate. What is the standard
form of the differential equation corresponding to
this problem, and what are p(t) and q(t)?
1
1
(A) S 0 − 500
S = 4, p(t) = − 500
, q(t) = 4
1
1
0
(B) S + 500 S = 4, p(t) = 500 , q(t) = 4
1
1
(C) S 0 + 500
S = −4, p(t) = 500
, q(t) = −4
(D) None of the above
Question 7: For the equation S 0 +
is F (t) and G (t)?
1
1
(A) F (t) = 500
t, G (t) = e − 500 t
1
1
t, G (t) = e 500 t
(B) F (t) = − 500
1
1
(C) F (t) = 500
t, G (t) = e 500 t
(D) None of the above
1
500 S
= 4 what
1
Question 8: The equation S 0 + 500
S = 4 is
equivalent to which equation below?
1
1
(A) (Se 500 t )0 = e 500 t
1
(B) (Se 500 t )0 = 4
1
1
(C) (Se 500 t )0 = 4e 500 t
(D) None of the above
Question 9: What is the general solution S to the
1
S = 4?
equation S 0 + 500
1
A) S = 4 + Ce − 500 t where C is a constant
1
(B) S = 2000 + Ce − 500 t , where C is a constant
1
(C) S = 2000 + Ce 500 t , where C is a constant
(D) None of the above
Question 10: Given S(0) = 300, what is C ?
A) −1700
(B) 1800
(C) 2200
(D) None of the above
Question 11: If the process continues indefinitely
how much salt will accumulate in the tank?
A) 2000
(B) 1800
(C) 2200
(D) None of the above
Key
1A, 2C, 3B, 4B, 5C, 6B, 7C, 8C, 9B, 10A, 11A