Question

a container of liquid with a volume of 100 ml is left open. the liquid evaporates at a rate of 10% per day. scientists graph the volume of the liquid ( y ) (in ml) over ( x ) days. what type of asymptote does this graph have, and what is its significance? choose 1 answer: a a horizontal asymptote at ( y = 0 ) tells us that the volume of the liquid in ml approaches 0. b a vertical asymptote at ( x = 0 ) tells us that the volume of the liquid in ml approaches 0. c a horizontal asymptote at ( y = 0 ) tells us that the volume of the liquid in ml approaches infinity. d a vertical asymptote at ( x = 0 ) tells us that the volume of the liquid in ml approaches infinity.

Explanation:

Step1: Define the decay function

The volume follows exponential decay: $y = 100(0.9)^x$

Step2: Analyze end behavior as $x\to\infty$

As $x$ increases, $(0.9)^x \to 0$, so $y\to0$.

Step3: Identify asymptote type

This is a horizontal asymptote at $y=0$, representing the volume approaching 0.

Answer:

A. A horizontal asymptote at $y = 0$ tells us that the volume of the liquid in mL approaches 0.