Question

a forest has 800 pine trees, but a disease is introduced that kills 25% of the pine trees in the forest every year. an ecologist graphs the number of trees y over x years. what type of asymptote does this graph have, and what is its significance? choose 1 answer: a a vertical asymptote at x = 0 tells us that the number of trees approaches infinity. b a horizontal asymptote at y = 0 tells us that the number of trees approaches infinity. c a horizontal asymptote at y = 0 tells us that the number of trees approaches 0. d a vertical asymptote at x = 0 tells us that the number of trees approaches 0.

Explanation:

Step1: Define decay function

The number of trees follows an exponential decay model: $y = 800(1-0.25)^x = 800(0.75)^x$

Step2: Analyze asymptote behavior

As $x \to +\infty$, $0.75^x \to 0$, so $y \to 0$. This is a horizontal asymptote.

Step3: Match to correct option

The asymptote $y=0$ means the tree count approaches 0.

Answer:

C. A horizontal asymptote at $y = 0$ tells us that the number of trees approaches 0.