5.3.1 Transaction Amount Components

At the heart of any decentralized platform lies its transactional activity. These transactions, whether they involve trading tokens, transferring data, or executing smart contracts, define the platform's vibrancy and utility. To gauge this vitality, we've designed a model that dives deep into the transactional behavior over time, presenting a clearer picture of platform engagement.

Let's break down the components:

• Actual Transactions (T_actual): This represents the real-world number of transactions that occur during month - t. It's the product of the platform's maximum potential transactions and a transaction profile factor, expressed as:

$$T_{actual} (t)=T_{max} (t)×K_{TX} (t)\ \ \ \ \ \ \ \tag{12}$$

• Maximum Potential Transactions (T_max): Envision an ideal scenario where every active user on the platform is transacting at their utmost capacity throughout month t. The total transactions from this perfect situation give us T_max

• Transaction Profile Factor (K_TX): This factor encapsulates the essence of our model. It mirrors the realistic transactional behavior on the platform. As users gradually familiarize themselves with the platform, their transaction frequency and volume are likely to increase. Over time, as they find their rhythm, their transactional activity might stabilize. This ebb and flow, this adoption curve, is captured within K_TX

The beauty of this transaction growth model lies in its nuanced yet streamlined approach. While K_TX (t) delves into the complexities of user behavior, adapting and evolving as the platform matures, our representation of active users is more straightforward. We assume that active users are a variable fraction of the total user base, oscillating within a predetermined range. Though this assumption offers a sturdy starting point, it's crucial to note that it can be further fine-tuned or validated with more granular data or insights.