Question

What relationship between supply rate and consumption rate must exist for the consumption of a resource to be sustainable?

Short answer

Answer: The consumption of a resource is considered sustainable when C ≤ S, where C is the consumption rate and S is the supply rate. This means that the consumption rate should be less than or equal to the supply rate to ensure the resource's sustainability for future generations.

Step-by-step solution

Define Supply Rate

Supply rate refers to the rate at which a resource is replenished or produced. In this scenario, it is the amount of the resource that becomes available for consumption per unit of time.

Define Consumption Rate

Consumption rate refers to the rate at which a resource is consumed or used up. In this scenario, it is the amount of the resource that is used per unit of time.

Determine Resource Sustainability

For the consumption of a resource to be sustainable, it must be used at a rate that does not exceed its replenishment rate. In other words, the consumption rate should be less than or equal to the supply rate.

Formulate the Relationship between Supply Rate and Consumption Rate

Based on the above understanding, the relationship between supply rate (S) and consumption rate (C) for a resource's consumption to be sustainable can be explained as follows: C ≤ S Where: C = Consumption Rate S = Supply Rate This relationship implies that consumption should be less than or equal to the supply of a resource to maintain its sustainability in the long run.

Key concepts

Supply Rate

The supply rate is a fundamental concept in understanding resource sustainability. It defines how quickly a resource is produced or replenished. Think of it as the speed at which new amounts of the resource become available for use. For instance, consider the rate at which trees grow in a forest or the amount of water collected during rainfall in a reservoir. These instances illustrate supply rates for timber and water respectively. To measure the supply rate, you would calculate how much of the resource is added per unit of time. This could be measured in gallons of water per day, tons of timber per year, or any similar unit depending on the resource in question. A consistent and healthy supply rate means that there is a stable inflow of the resource, which is crucial for sustainability planning.

Consumption Rate

On the other hand, the consumption rate defines the pace at which a resource is used up. Just like you might measure how much of a resource is created or replenished, you also measure how fast it is being consumed. This usage rate is commonly seen in daily life; for example, the rate at which you consume electricity at home or the amount of gasoline used by vehicles. The consumption rate can vary greatly between different resources and even for the same resource depending on human activities or natural factors. For sustainability, understanding the consumption rate is as critical as knowing the supply rate because it helps identify whether the current usage is sustainable or not. If resources are depleted faster than they are replenished, that's a red flag for unsustainability.

Sustainability Equation

The sustainability equation is key to understanding if resource use can continue into the future without depleting the reserves. It represents the balance between supply and consumption rates. Mathematically, it says that for sustainability, the consumption rate (C) should not exceed the supply rate (S). This relationship can be expressed as:\[ C \leq S \]This simple inequality serves as a deciding line in sustainability discussions.

• If the consumption rate equals the supply rate (\( C = S \)), the resource is being used exactly at its rate of replenishment. This is marginally sustainable but can be risky if either rate changes.
• If the consumption rate is less than the supply rate (\( C < S \)), the use is sustainable. The resource is being consumed slower than it is supplied, allowing reserves to build or remain constant over time.
• If the consumption rate exceeds the supply rate (\( C > S \)), the use is unsustainable, leading to depletion of the resource over time.

Ensuring that usage aligns with this equation is fundamental for preserving resources for future generations.