Water Resource Issues: Mathematical Modelling for Edexcel A-Level | 水资源问题：Edexcel A-Level 数学建模

📚 Water Resource Issues: Mathematical Modelling for Edexcel A-Level | 水资源问题：Edexcel A-Level 数学建模

Water resource issues such as scarcity, pollution and changing demand are often discussed in geography, but they also provide rich contexts for A-Level Mathematics. This article applies core Edexcel A-Level techniques – linear models, exponentials, differentiation, integration, probability and optimisation – to water problems. Each section pairs an English explanation with a Chinese translation.

水资源短缺、污染和需求变化等问题常在地理中讨论，但它们也为 A-Level 数学提供了丰富的应用情境。本文将 Edexcel A-Level 核心方法（线性模型、指数函数、微分、积分、概率和优化）用于水资源问题。每节均提供英文解释与中文对照。

1. Water as a Natural Resource: Key Quantities | 作为自然资源的水：关键量

In Edexcel A-Level Mathematics, applied questions often begin with units and basic modelling. Water problems use flow rate Q in cubic metres per second (m³/s), per capita consumption in litres per person per day (L/person/day), and storage volume V in cubic metres (m³). You must be able to convert between these units accurately.

在 Edexcel A-Level 数学中，应用题通常从单位和基本建模开始。水问题使用流量 Q (m³/s)、人均用水量 (L/人/日) 和蓄水量 V (m³)。你必须能够准确进行这些单位之间的换算。

For example, a flow of 0.5 m³/s over one day delivers 0.5 × 86 400 = 43 200 m³ of water. Since 1 m³ = 1000 litres, this is 43 200 000 litres. Such conversions are common in resource management questions.

例如，0.5 m³/s 的流量持续一天可输送 0.5 × 86 400 = 43 200 m³ 的水。由于 1 m³ = 1000 升，即 43 200 000 升。此类换算在资源管理问题中很常见。

2. Linear Models of Water Consumption | 水资源消耗的线性模型

A linear model assumes that water consumption changes by a constant amount each time period. The equation W = mt + c links consumption W to time t, where m is the gradient and c is the intercept. Given two data points (t₁, W₁) and (t₂, W₂), the gradient is m = (W₂ − W₁)/(t₂ − t₁).

线性模型假设水资源消耗量在每个时间段内以恒定数量变化。方程 W = mt + c 将用水量 W 与时间 t 联系起来，其中 m 是斜率，c 是截距。给定两个数据点 (t₁, W₁) 和 (t₂, W₂)，斜率为 m = (W₂ − W₁)/(t₂ − t₁)。

W = mt + c

Linear models are useful for short-term predictions, but they can be unrealistic over long periods because they assume no percentage growth. Exam questions often ask you to interpret m and c in context.

线性模型适用于短期预测，但长期来看可能不现实，因为它假设没有百分比增长。试题常要求你在实际情境中解释 m 和 c 的含义。

3. Exponential Growth and Decay in Water Demand | 水资源需求的指数增长与衰减

When water demand increases by a fixed percentage, an exponential model is more appropriate. The continuous form is P = P₀e^kt, where P₀ is the initial quantity, k is the continuous growth rate and t is time. For example, if k = 0.03 per year, demand grows by about 3% per year continuously.

当水资源需求按固定百分比增长时，指数模型更合适。连续形式为 P = P₀e^kt，其中 P₀ 为初始量，k 为连续增长率，t 为时间。例如，若 k = 0.03/年，需求约按每年 3% 连续增长。

P = P₀e^kt

The doubling time is the time needed for demand to double. It is found by solving e^kt = 2, which gives t = ln 2 / k. If k = 0.03, the doubling time is approximately 23.1 years

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