the pasadena high school biology club is plan...
the pasadena high school biology club is planning a trip to yosemite national park. the trip will cost $300 per club member plus an $800 deposit. which of the following graphs models the total average cost of the trip per club member?
Answer
# Explanation:
## Step1: Define the cost - function
Let $x$ be the number of club members. The total cost $C$ of the trip is $C = 300x+800$. The average cost per member $A$ is $A=\frac{300x + 800}{x}=300+\frac{800}{x}$.
## Step2: Analyze the behavior of the function
As $x$ (the number of members) approaches infinity, $\frac{800}{x}$ approaches 0. So the horizontal - asymptote of the function $y = 300+\frac{800}{x}$ is $y = 300$. Also, when $x = 1$, $A=300 + 800=1100$. As $x$ increases, the value of $A$ decreases and gets closer and closer to 300 but never reaches 300.
# Answer:
The graph that has a horizontal asymptote at $y = 300$ and starts at a high - value for small $x$ values (since when $x = 1$, the average cost is high) and decreases as $x$ increases is the correct graph. Without seeing the full options, but based on the analysis, the function $y=300+\frac{800}{x}$ is a rational function with a horizontal asymptote at $y = 300$ and is a decreasing function for $x>0$.