Average daily growth = r + 1.375. But r is unknown. - High Altitude Science

Understanding the Context

But what if r remains unknown? How do you interpret and apply this growth model effectively when the core variable is hidden? In this article, we’ll break down the implications of the formula, explore how to interpret average daily growth even without knowing r, and offer practical advice for users and analysts alike.

What Does the Formula Mean?

At first glance, r + 1.375 appears straightforward. However, r represents the daily growth rate—typically expressed as a decimal or percentage. Adding 1.375 suggests this formula models compounded growth with a baseline daily increase of 1.375 units (which could be absolute growth, relative percentage, or normalized scaling depending on context).

Key Insights

Because r is unknown, we treat it as a variable input rather than a fixed constant. This flexibility makes the formula useful for modeling unknown but stable growth trajectories—until more data clarifies r.

Why r Matters (and Maybe Doesn’t)

Traditional compound growth formulas like A = P(1 + r)^n rely heavily on r to calculate future value. But in the expression r + 1.375, r may not represent compounding; rather, it could capture baseline daily increment, especially in simple trend analysis or when paired with linear projections.

Since r is unknown, consider the following:

Final Thoughts

• Without r, growth is probabilistic or estimated based on observed averages.
  
• Small values of r may indicate slow, steady growth—like a stable customer base or modest revenue increase.
  
• Larger r values suggest faster acceleration, but without calibration, projections become speculative.

Practical Interpretation: Using the Formula Even When r is Unknown

Because r isn’t fixed, you can still analyze trends by:

1. Identifying Growth Patterns

Plot daily values using the formula: D_t = D_{t-1} × (1 + r) + 1.375
Even without knowing r, observing whether growth stabilizes or spikes over time helps identify shifts in momentum.

2. Comparing Across Periods

If multiple time series follow r + 1.375, comparing average daily values reveals relative performance. Sudden deviations or consistent deviations signal underlying changes in growth drivers.