Solve the problem.
-A tank initially contains 100 gal of brine in which 40 lb of salt are dissolved. A brine containing 2 lb/gal of salt runs into the tank at the rate of 4 gal/min. The mixture is kept uniform by stirring and flows out of the tank at
The rate of 3 gal/min. Find the solution to the differential equation that models the mixing process.
A) $y = 4 ( 50 + t ) - \frac { C } { ( 100 + t ) ^ { 3 } }$
B) $y = 2 ( 100 + t ) - \frac { 10 ^ { 8 } } { ( 100 + t ) ^ { 3 } }$
C) $y = 4 ( 50 + t ) - \frac { 10 ^ { 8 } } { ( 100 + t ) ^ { 3 } }$
D) $y = 2 ( 100 + t ) - \frac { C } { \left( 100 + t ^ { 3 } \right) }$

Question

Solve the problem.
-A tank initially contains 100 gal of brine in which 40 lb of salt are dissolved. A brine containing 2 lb/gal of salt runs into the tank at the rate of 4 gal/min. The mixture is kept uniform by stirring and flows out of the tank at
The rate of 3 gal/min. Find the solution to the differential equation that models the mixing process. 
A) $y = 4 ( 50 + t ) - \frac { C } { ( 100 + t ) ^ { 3 } }$
B) $y = 2 ( 100 + t ) - \frac { 10 ^ { 8 } } { ( 100 + t ) ^ { 3 } }$
C) $y = 4 ( 50 + t ) - \frac { 10 ^ { 8 } } { ( 100 + t ) ^ { 3 } }$
D) $y = 2 ( 100 + t ) - \frac { C } { \left( 100 + t ^ { 3 } \right) }$

Quizplus · Accepted Answer

The differential equation for the salt in the tank is derived from the rate of salt entering and leaving. The solution reflects the initial condition and the rates of change.

Solve the Problem y=4(50+t)−C(100+t)3y = 4 ( 50 + t ) - \frac { C } { ( 100 + t ) ^ { 3 } }y=4(50+t)−(100+t)3C​

Solve the Problem $y = 4 ( 50 + t ) - \frac { C } { ( 100 + t ) ^ { 3 } }$