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)=15/30+x respresents the concentration of acid,A, in the mixture as x amount of water is added
To determine a reasonable domain and range for this scenario, let's first understand the context of the problem. We have a 30 milliliter solution that is 50% acid (presumably by volume). We then add x amount of water to the solution, resulting in a new concentration of acid in the mixture, represented by A(X).
The equation given is A(X) = (15/30) + x, which expresses the concentration of acid in the mixture as a function of the amount of water added.
Domain:
In this scenario, the amount of water added, represented by x, should be in a reasonable range. Since we cannot add negative amounts of water, the domain of x should be x ≥ 0. We should only consider adding non-negative amounts of water to the solution.
Range:
The range of the function A(X) represents the possible concentrations of acid in the mixture. Since we are given that the initial solution is 50% acid, the concentration of acid can vary from 0% (if we add a large amount of water) up to 100% (if we add no water at all). Hence, the range of A(X), represented by the concentration of acid, is 0% ≤ A(X) ≤ 100%.
Therefore, a reasonable domain for this scenario is x ≥ 0, and a reasonable range is 0% ≤ A(X) ≤ 100%.