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A wholesaler uses the function [tex]f(x) = 8 \sqrt{x}[/tex] to determine the cost, in dollars, to buy [tex]x[/tex] gallons of lemonade. Find and interpret the given function values and determine an appropriate domain for the function.

Round your answers to the nearest cent.

[tex]f(0) = \quad \, \square \, \, \, [/tex], meaning the cost of buying [tex]\square[/tex] gallons of lemonade would be \$ [tex]\square[/tex]. This interpretation [tex]\square[/tex] in the context of the problem.

[tex]f(20) = \quad \, \square \, \, \, [/tex], meaning the cost of buying [tex]\square[/tex] gallons of lemonade would be \$ [tex]\square[/tex]. This interpretation [tex]\square[/tex] in the context of the problem.

[tex]f(24.5) = \quad \, \square \, \, \, [/tex], meaning the cost of buying [tex]\square[/tex] gallons of lemonade would be \$ [tex]\square[/tex].

This interpretation [tex]\square[/tex] in the context of the problem.

Based on the observations above, it is clear that an appropriate domain for the function is



Answer :

GinnyAnswer
The wholesaler uses the function [tex]\( f(x) = 8 \sqrt{x} \)[/tex] to determine the cost, in dollars, to buy [tex]\( x \)[/tex] gallons of lemonade. Let's find and interpret the given function values and determine an appropriate domain for the function.

1. [tex]\( f(0) = \)[/tex]:
[tex]\[ f(0) = 8 \sqrt{0} = 0.0 \][/tex]
meaning the cost of buying [tex]\( 0 \)[/tex] gallons of lemonade would be \[tex]$ \( 0.00 \). This interpretation makes sense in the context of the problem because no lemonade is bought so the cost is \( \$[/tex]0 \).

2. [tex]\( f(20) = \)[/tex]:
[tex]\[ f(20) = 8 \sqrt{20} = 35.77708763999664 \approx 35.78 \][/tex]
meaning the cost of buying [tex]\( 20 \)[/tex] gallons of lemonade would be \[tex]$ \( 35.78 \). This interpretation makes sense in the context of the problem as the cost for \( 20 \) gallons of lemonade is calculated. 3. \( f(24.5) = \): \[ f(24.5) = 8 \sqrt{24.5} = 39.59797974644666 \approx 39.60 \] meaning the cost of buying \( 24.5 \) gallons of lemonade would be \$[/tex] [tex]\( 39.60 \)[/tex]. This interpretation makes sense in the context of the problem as the cost for [tex]\( 24.5 \)[/tex] gallons is calculated.

Based on the observations above, the domain of the function should be determined.

Since the square root function is only defined for non-negative numbers and cost cannot be calculated for a negative number of gallons, the appropriate domain for the function is:
[tex]\[ [0, \infty) \][/tex]

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