21
RCMultiple Choice

Expected Value — Cumulative exam

Question 21 • CREDIT RE-SEAT MNPS Integrated Math III IC S2 26-27

A chemist has 500 mL of a 30% acid solution. She adds x milliliters of a 10% acid solution. Which statement is true about the graph of the function that represents the concentration of the final solution?

Answer
A
The horizontal asymptote y = 30 means that the final concentration will always be less than 30%.
B
The horizontal asymptote y = 10 means that the final concentration will always be greater than 10%.
C
The vertical asymptote x = 500 means that the volume of the solution will always be greater than 500 mL.
D
The vertical asymptote x = 0 means that the volume of the solution will always be greater than 0 mL.

Explanation

The mixture contains 150 mL of acid initially, and adding x mL of 10% solution adds 0.1x mL of acid. Its concentration is 100(150 + 0.1x)/(500 + x) percent, which approaches 10% as x grows. For every finite x ≥ 0, the original 30% solution keeps the final concentration greater than 10%, so choice B is true.

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