Part 1: Your Water Consumption Survey Result And Applying Ma

Part 1: Your water consumption survey result and applying mathematical

Calculate and analyze water usage at home based on survey data and mathematical functions, including filling in variables, understanding water collection processes, modeling these processes with functions, graphing data, and interpreting results related to water collection and household consumption.

Paper For Above instruction

In the context of water conservation and efficient resource management, understanding individual and household water usage is critical. The survey results presented highlight typical water consumption patterns at home, including activities such as bathing, teeth brushing, face washing, shaving, dishwashing, laundry, and toilet flushing. These data points offer a comprehensive picture of daily water use, and analyzing them provides insight into potential conservation strategies. Additionally, modeling the water collection process—specifically, how many gallons a person can gather from the river over multiple walks—provides a valuable quantitative framework for understanding water scarcity issues, especially in regions like Ethiopia where access to clean water remains a challenge.

Assessment of Water Use at Home

The survey reveals that activities at home consume varying amounts of water. A full bathtub typically uses about 36 gallons, whereas showers—especially with water-saving showerheads—use approximately 2 gallons per minute compared to older models utilizing up to 5 gallons per minute. Shortening shower duration and installing efficient fixtures can thus significantly reduce water consumption. For activities like teeth brushing and face washing, turning off faucets when not needed saves water, with typical use being less than 1 and 1 gallon, respectively. Shaving also consumes about 1 gallon when faucets are turned off during the process.

Dishwasher use is another significant water-consuming activity, with new energy-efficient models using as little as 6 gallons per cycle, whereas older models may require up to 16 gallons. Hand washing dishes can vary widely—from 8 to 27 gallons—depending on technique and efficiency. Implementing strategies like scrapping food beforehand, soaking dishes, and using two basins can minimize water waste. Laundry, a major household activity, consumes around 25 gallons per load with newer washers, compared to 40 gallons with older models. Toilet flushes—another critical water use—average about 3 gallons per flush, with modern low-flow toilets reducing this to approximately 1.6 gallons.

Understanding these data allows consumers to identify pathways for conservation, such as installing low-flow fixtures, fixing leaks, and adopting water-efficient behaviors. Collectively, these small modifications contribute to substantial savings in household water usage, reduce utility bills, and alleviate pressure on local water sources.

Understanding Water Collection and Quantitative Modeling

The second part of the assignment focuses on developing a mathematical model for water collection from a river, which is especially relevant in water-scarce settings. The variables n, g, m, t, d, and h represent the number of walks, gallons collected per walk, miles walked, hours spent walking, days, and total gallons at home, respectively. Filling in these variables clarifies the water collection process. For example, one might state:

  • In n walks to the river, you get g gallons of water.
  • When you walk m miles, you get g gallons.
  • n walks to the river takes t hours.
  • After d days, you have h gallons of water at home.

By correlating the number of walks (n) with the gallons collected (g), one can define a function f(n) that models the water collection process. The input of this function is n (number of walks), and the output is g(n), the total gallons collected after n walks.

Empirical data from the survey suggests that each walk yields a certain average gallon amount, which allows plotting a graph of f(n). For instance, if each walk yields roughly 10 gallons, the data points would reflect that linear relationship, making the graph linear with a positive slope—indicating more walks result in more water. The x-axis units are the number of walks, and the scale could be set in integers, for example, ticks every one walk. The y-axis represents gallons of water collected, with appropriate scale for the gallons obtained per number of walks.

The slope of the line in the graph indicates the rate at which water is collected per walk—if the slope is 10, then each walk yields approximately 10 gallons. The slope's sign (positive or negative) indicates whether increasing walks increase or decrease water collection—here, it would be positive. The y-intercept, where the line crosses the y-axis, represents the initial amount of water at home before any walks—possibly zero if starting fresh or the existing stored water.

The equation of the line in slope-intercept form would be g(n) = m n + b, where m is the slope and b the y-intercept. Using this model, one can estimate the gallons of water obtained after any number of walks, such as 15 or 38, by substituting into the equation. For example, if g(n) = 10 n + 0, then after 15 walks, total gallons are 150.

Furthermore, the model allows for calculating the water obtained after 9 or 52 walks and understanding the significance of the functions. If the minimum daily water requirement for a refugee camp is specified—say, 15 liters (~4 gallons)—one can determine how many walks are necessary to achieve that amount, i.e., solving for n in the function. This model offers insights into the feasibility of water collection strategies and highlights the importance of efficiency and reducing the number of walks needed.

Analyzing average household water usage, if an average family uses about 300 gallons daily, and each walk yields 10 gallons, approximately 30 walks per day are needed, an impractical figure in many situations. This emphasizes just how critical it is to adopt water-saving measures at every stage, from collection to household use. Comparing the individual water use survey with the collection model allows for a holistic understanding of water management challenges faced in vulnerable communities.

Graphing and Interpreting the Data

Using graphing tools such as Desmos.com, the relation between the number of walks (n) and gallons of water collected (g(n)) can be visualized. The units on the x-axis are the number of walks (integers), with a scale that represents each tick as one walk. The y-axis units are gallons, with scale suited for the range of water collected. The window should encompass the data points, with appropriate margins to visualize the trend. Values that the graph should exclude include negative numbers of walks (impossible) and excessive values where data may be unreliable.

The slope indicates the average water gained per walk, with a positive slope corresponding to an increasing amount of water collected with each additional walk. For example, if the slope is 10, then each walk adds an average of 10 gallons. The y-intercept, likely zero or a small initial amount, signifies the starting water stores or the baseline before collection.

The slope-intercept form captures these relationships precisely, enabling predictions and planning. For instance, after 15 walks, total water would be 150 gallons, and after 38 walks, 380 gallons (assuming the slope of 10). Calculating specific function values like f(9) and f(52) provides precise estimates, aiding decision-making in water resource planning.

Implications for Water Management in Crisis Settings

The modeled relationships are crucial in contexts like refugee camps, where water access is limited. The water requirement of approximately 4 gallons per person per day, as suggested by the CNN article, can be used to estimate the number of walks required to meet daily needs. For example, if each walk yields 10 gallons, about half a walk suffices, indicating the importance of efficient collection strategies. Conversely, if water yields are lower, alternative solutions or improved collection techniques become necessary.

Understanding these quantitative relationships supports developing policies for water distribution, investment in better collection infrastructure, and community education on water conservation. The integration of household water use data with collection models underscores the importance of a multifaceted approach to managing scarce water resources effectively.

Overall, this exercise illustrates how mathematical modeling and data analysis can inform practical solutions to global water issues, emphasizing conservation, efficiency, and strategic planning as essential components of sustainable water management.

References

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  • United Nations. (2015). Sustainable Development Goal 6: Clean water and sanitation. https://sdgs.un.org/goals/goal6
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