A Microbiologist Must Prepare a Culture Medium in Which to Grow

question 75

Multiple Choice

A microbiologist must prepare a culture medium in which to grow a certain type of bacteria. The percent of salt contained in this medium is given by $S = 12 x y z$ where $x , y,$ and $z$ are the nutrient solutions to be mixed in the medium. For the bacteria to grow, the medium must be 13% salt. Nutrient solutions $x , y,$ and $z$ cost $1, $2, and $3 per liter, respectively. How much of each nutrient solution should be used to minimize the cost of the culture medium?

• A) \(\begin{array} { l }
• x = \sqrt [ 3 ] { 0.065 } \approx 0.402 L \\
• y = \sqrt [ 3 ] { 0.065 } \approx 0.201 L \\
• z = \sqrt [ 3 ] { 0.065 } \approx 0.134 L
• \end{array}\)
• B) \(\begin{array} { l }
• x = \sqrt [ 3 ] { 0.035 } \approx 0.327 L \\
• y = \sqrt [ 3 ] { 0.165 } \approx 0.548 L \\
• z = \sqrt [ 3 ] { 0.015 } \approx 0.2466 L
• \end{array}\)
• C) \(\begin{array} { l }
• x = \sqrt [ 3 ] { 0.065 } \approx 0.402 L \\
• y = \sqrt [ 3 ] { 0.165 } \approx 0.548 L \\
• z = \sqrt [ 3 ] { 0.055 } \approx 0.380 L
• \end{array}\)
• D) \(\begin{array} { l }
• x = \sqrt [ 3 ] { 0.025 } \approx 0.292 L \\
• y = \sqrt [ 3 ] { 0.035 } \approx 0.327 L \\
• z = \sqrt [ 3 ] { 0.115 } \approx 0.486 L
• \end{array}\)
• E) \(\begin{array} { l }
• x = \sqrt [ 3 ] { 0.165 } \approx 0.548 L \\
• y = \sqrt [ 3 ] { 0.165 } \approx 0.548 L \\
• z = \sqrt [ 3 ] { 0.265 } \approx 0.642 L
• \end{array}\)

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Definitions:

Carbons

The chemical element with atomic number 6, fundamental to life, and the basis of organic chemistry.

Micelle

An aggregate of surfactant molecules dispersed in a liquid colloid, forming a molecular assembly that can solubilize hydrophobic molecules in its hydrophobic core.

Hydrophobic

Characteristic of molecules or substances that do not readily mix with water.

Hydrophilic

Describes molecules or substances that are attracted to water and dissolve well in it.