A Large Mixing Tank Initially Contains 100 Gallons of Water $A ( t )$

question 5

Multiple Choice

A large mixing tank initially contains 100 gallons of water in which 30 pounds of salt have been dissolved. Another brine solution is pumped into the tank at the rate of 4 gallons per minute, and the resulting mixture is pumped out at the same rate. The concentration of the incoming brine solution is 2 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) \(\frac { d A } { d t } = 8 - .02 A\)
• B) \(\frac { d A } { d t } = 8 - .04 A\)
• C) \(\frac { d A } { d t } = 4 - .04 A\)
• D) \(\frac { d A } { d t } = 2 - .04 A\)
• E) \(\frac { d A } { d t } = 4 - .08 A\)

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Definitions:

Variance

An index of variability in a set of data, established by taking the average squared deviation from the mean.

Tchebysheff's Theorem

A theorem that states for any real numbers k > 1, at least (1-1/k^2) of the data values fall within k standard deviations of the mean for any distribution.

Empirical Rule

A statistical rule stating that for a normally distributed dataset, about 68% of values fall within one standard deviation, 95% within two, and 99.7% within three standard deviations from the mean.

Tchebysheff's Theorem

A mathematical formula that determines the minimum proportion of values that lie within a specified number of standard deviations from the mean, for any distribution.