A 300-gallon tank is full of a solution containing 35 pounds of concentrate. Starting at time distilled water is added to the tank at a rate of 30 gallons per minute, and the well-stirred Solution is withdrawn at the same rate. Find the amount of concentrate Q in the solution as a function Of t.
A)$Q = e ^ { ( 1 / 30 ) t }$
B) $Q = 30 e ^ { - ( 1 / 10 ) t }$
C) $Q = 300 e ^ { - ( 1 / 10 ) z }$
D) $Q = 35 e ^ { - ( 1 / 10 ) t }$
E) $Q = e ^ { - ( 1 / 35 ) z }$

Question

A 300-gallon tank is full of a solution containing 35 pounds of concentrate. Starting at time distilled water is added to the tank at a rate of 30 gallons per minute, and the well-stirred Solution is withdrawn at the same rate. Find the amount of concentrate Q in the solution as a function Of t. 
A)$Q = e ^ { ( 1 / 30 ) t }$
B) $Q = 30 e ^ { - ( 1 / 10 ) t }$
C) $Q = 300 e ^ { - ( 1 / 10 ) z }$
D) $Q = 35 e ^ { - ( 1 / 10 ) t }$
E) $Q = e ^ { - ( 1 / 35 ) z }$

Quizplus · Accepted Answer

The correct answer is D) $Q = 35 e ^ { - ( 1 / 10 ) t }$. This is derived from the differential equation modeling the rate of change of the amount of concentrate in the tank, considering the dilution effect of adding distilled water while maintaining a constant volume. The initial amount of concentrate is 35 pounds, and the exponential decay factor comes from the rate of water exchange relative to the tank's volume.

A 300-Gallon Tank Is Full of a Solution Containing 35 Q=e(1/30)tQ = e ^ { ( 1 / 30 ) t }Q=e(1/30)t

A 300-Gallon Tank Is Full of a Solution Containing 35 $Q = e ^ { ( 1 / 30 ) t }$