A Large Mixing Tank Initially Contains 1000 Gallons of Water $A ( t )$

question 29

Multiple Choice

A large mixing tank initially contains 1000 gallons of water in which 40 pounds of salt have been dissolved. Another brine solution is pumped into the tank at the rate of 5 gallons per minute, and the resulting mixture is pumped out at the same rate. The concentration of the incoming brine solution is 3 pounds of salt per gallon. If $A ( t )$ represents the amount of salt in the tank at time t, the correct differential equation for A is

• A) \(\frac { d A } { d t } = 3 - .005 A\)
• B) \(\frac { d A } { d t } = 5 - .05 A\)
• C) \(\frac { d A } { d t } = 15 - .005 A\)
• D) \(\frac { d A } { d t } = 3 - .05 A\)
• E) \(\frac { d A } { d t } = 15 + .05 A\)

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Definitions:

Confidence Interval

A variety of values, based on statistics from a sample, which is conjectured to envelop an obscure population parameter.

P-value

A statistical concept indicating the probability of observing data as extreme as those seen, if the null hypothesis were true, used in hypothesis testing.

Maximum Oxygen Uptake

The highest amount of oxygen an individual can utilize during intense or maximal exercise, indicating aerobic endurance capacity.

Normal Distribution

A bell-shaped curve, which is symmetric about the mean, depicting the distribution of many types of data.