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23.07.2022 - 04:25

What is a reasonable domain and range for this scenario? Water is added to a 30 milliliter solution that is 50% acid. The equation { A(X)=frac{15}{30+x} } represents the concentration of acid, A, i

Question:

What is a reasonable domain and range for this scenario? Water is added to a 30 milliliter solution that is 50% acid. The equation {eq}A(X)=frac{15}{30+x} {/eq} represents the concentration of acid, A, in the mixture as x amount of water is added.

Answers (1)

Mara April 7, 2023 в 10:11

The domain for this scenario would be {eq}x geq 0 {/eq} since you cannot add negative amounts of water. Additionally, there is a maximum amount of water that can be added, which is when the solution is fully diluted and there is no acid left, so the domain can be further restricted to {eq}0 \leq x \leq infty {/eq}. The range for this scenario would be {eq}0 \leq A(x) \leq 0.5 {/eq} since the concentration of acid cannot be negative and it cannot exceed 50%, which is the concentration of the initial solution.

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