Question A wholesaler uses the function \( f(x)=8 \sqrt{x} \) to determine the cost, in dollars, to buy \( x \) 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. Answer Atempt out of 2 \( f(0)=\square \), meaning the cost of buying \( \square \) gallons of lemonade would be \( \$ \square \). This interpretation \( f(85)=\square \), meaning the cost of buying \( \square \) gallons of lemonade would be \( \$ \square \). This interpretation \( f(62.5)=\square \) in the context of the problem. lemonade would be \( \$ \square \). This interpretation \( \square \) in the context of the problem. Based on the observations above, it is clear that an appropriate domain for the function is \( \square \)

When evaluating the function at \( f(0) \), we find \( f(0) = 8 \sqrt{0} = 0 \), meaning the cost of buying \( 0 \) gallons of lemonade would be \( \$0.00 \). This interpretation illustrates that if no lemonade is purchased, there is no cost incurred. Now, for \( f(85) \), we have \( f(85) = 8 \sqrt{85} \approx 69.80 \), meaning the cost of buying \( 85 \) gallons of lemonade would be approximately \( \$69.80 \). This interpretation reflects bulk purchasing, leading to savings from buying a larger quantity. Moving on to \( f(62.5) \), we get \( f(62.5) = 8 \sqrt{62.5} \approx 62.63 \), meaning the cost of buying \( 62.5 \) gallons of lemonade would be approximately \( \$62.63 \). This demonstrating a precise calculation for purchasing a non-integer quantity of lemonade. In light of these observations, it is clear that an appropriate domain for the function is \( [0, \infty) \), as it makes practical sense that the quantity of lemonade cannot be negative.