Question

A pharmacist has 80 milliliters of a 30% saline solution. The graph shows the percentage concentration after adding x milliliters of a 10% saline solution. Which statement is true about the graph of the function?

mc018-1.jpg
The vertical asymptote x = 30 means the concentration will always be less than 30%.
The vertical asymptote x = 10 means the volume will always be greater than 10 milliliters.
The y-intercept means the concentration will remain 30% if no solution is added.
The y-intercept means the concentration will always be less than 30%.

Answer 1

Write the concentration after adding x mL:

y = (24 + 0.10x)/(80 + x) because 0.30·80 = 24 mL salt initially.

Evaluate the y‑intercept: y(0) = 24/80 = 0.30 = 30%. So the correct statement is:

"The y-intercept means the concentration will remain 30% if no solution is added."

(The other statements are incorrect: the denominator 80 + x gives no vertical asymptote at x = 30, and the concentration equals 30% at x = 0 so it is not “always” less than 30%.)