1. as the population gets larger and larger, what happens to the amount of water available?
2.5 f(200)= 200 500 =2.5, which is half of 5
if the population doubles trrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr
2. what happens to the amount of available water when the population doubles (is multiplied by 2)?
when the population doubles is multiplied by 2, the amount of available water per person
3. what does f(50) mean in this context?
when there are 50 people,.....
4. where is the horizontal asymptote in this graph? what does it represent in this context?
as the population increases,___

Question

Accepted Answer

### Question 1
# Explanation:
## Step1: Analyze the graph trend
The graph of $ f(x) $ (amount of water) vs $ x $ (population) is a curve that decreases as $ x $ increases and approaches a horizontal line (asymptote) as $ x \to \infty $.
## Step2: Determine the behavior
As population ($ x $) gets larger, the amount of water ($ y = f(x) $) decreases and approaches the horizontal asymptote (gets closer to a minimum non - zero or zero value, from the graph's shape).
# Answer:
As the population gets larger and larger, the amount of water available decreases and approaches the horizontal asymptote (gets closer to a very small, nearly constant amount or zero, depending on the asymptote's value).

### Question 2
# Explanation:
## Step1: Understand the function relationship
From the given $ f(200)=\frac{500}{200} = 2.5 $ (assuming a reciprocal - like relationship, maybe $ f(x)=\frac{k}{x} $, here when $ x = 100 $, if $ f(100) = 5 $, then $ k = 500 $).
## Step2: Analyze the doubling effect
If population $ x $ doubles (say from $ x_1 $ to $ x_2 = 2x_1 $), and $ f(x)=\frac{k}{x} $, then $ f(x_2)=\frac{k}{2x_1}=\frac{1}{2}\times\frac{k}{x_1}=\frac{1}{2}f(x_1) $. So when the population doubles, the amount of available water per person (or total available water, depending on the function's definition) is halved.
# Answer:
When the population doubles, the amount of available water is halved (assuming the function is of the form $ f(x)=\frac{k}{x} $, as seen from $ f(200) = 2.5 $ being half of $ f(100)=5 $).

### Question 3
# Explanation:
## Step1: Recall function notation
In the context of $ f(x)=y $, where $ x $ is population and $ y $ is amount of water available, $ f(50) $ means we are evaluating the function at $ x = 50 $.
## Step2: Interpret in context
So $ f(50) $ represents the amount of water available when the population is 50.
# Answer:
$ f(50) $ means the amount of water available when the population is 50.

### Question 4
# Explanation:
## Step1: Identify the horizontal asymptote
A horizontal asymptote of a function $ y = f(x) $ is a horizontal line $ y = L $ that the graph of the function approaches as $ x\to\pm\infty $. From the graph, as $ x$ (population) increases, the graph approaches the $ x $ - axis (or a horizontal line $ y = 0 $ or a small positive $ y $ - value).
## Step2: Interpret in context
In this context, the horizontal asymptote (say $ y = 0 $ or a very small positive number) represents the minimum amount of water available as the population becomes extremely large. As the population increases without bound, the amount of water available approaches this asymptote, meaning it gets closer and closer to this minimum amount (could be a theoretical minimum or the amount that can't be reduced below a certain limit).
# Answer:
The horizontal asymptote is the horizontal line that the graph approaches as $ x$ (population) approaches infinity (likely $ y = 0 $ or a small positive $ y $ - value). In this context, it represents the minimum amount of water available as the population becomes extremely large (the amount of water approaches this value as population grows without bound).

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QUESTION IMAGE

Question

Explanation:

Question 1

Step1: Analyze the graph trend

Step2: Determine the behavior

Step1: Understand the function relationship

Step2: Analyze the doubling effect

Step1: Recall function notation

Step2: Interpret in context

Answer:

Question 2