If increased or improved business growth is your objective this information is highly relevant to you because it introduces a growth framework that leverages the concept of exponential growth, a principle that can significantly amplify business outcomes over time. By understanding and applying this framework, you can potentially achieve growth at a scale and speed that far surpasses traditional linear strategies… but first you must read, understand, and apply these insights.
Within ‘Invincible” I’ve presented a nine-step framework for growth. The framework is not just a random, arbitrary alignment of ideas. The process outlined in Invincible builds on the power of exponential growth. Below I will explain exponential growth from a ‘nerdy’ mathematical point of view and also a practical view. In my private Facebook group I posted a video walkthrough showing how this process applies specifically to the nine-step framework and why you MUST focus on this specific game plan to achieve predictable growth.
In the scenario of exponential growth, you start with a single penny ($0.01). Each day, the amount you have doubles. This means:
- On Day 1, you have $0.01.
- On Day 2, you have $0.02 (2 times $0.01).
- On Day 3, you have $0.04 (2 times $0.02).
- This doubling continues each day for 31 days.
The formula for exponential growth here is F=P⋅2n−1F=P⋅2n−1, where:
- FF is the final amount,
- PP is the initial principal balance ($0.01),
- nn is the number of time periods (days).
Linear Growth: A Penny Added Every Day
In contrast, with linear growth, you start with a penny and add another penny to the total each day. So:
- On Day 1, you have $0.01.
- On Day 2, you have $0.02 ($0.01 + $0.01).
- On Day 3, you have $0.03 ($0.02 + $0.01).
- This addition continues each day for 31 days, leading to a final amount of $0.31.
The formula for linear growth is F=P+(n−1)⋅dF=P+(n−1)⋅d, where:
- FF is the final amount,
- PP is the initial principal balance ($0.01),
- dd is the daily addition ($0.01),
- nn is the number of days.
* Comparing the Two – this is what actually matters…
To illustrate the difference in growth between these two methods over 31 days, let’s calculate the final amount for both exponential and linear growth scenarios.
The difference between exponential and linear growth over 31 days is stark:
- Linear Growth: Starting with a penny and adding another penny each day for 31 days results in a final amount of just $0.31. <—
- Exponential Growth: Starting with a penny and doubling it every day for 31 days results in a final amount of $10,737,418.24. <—
After 31 days of effort which potential would you rather have? The $10,737,418.24 or the .31? If growth is your goal the answer is obvious.
Lets Be Reasonable
Admittedly, grabbing that many pennies may be impossible. But this isn’t about encouraging anyone to go on a mad search for pennies in streets and parking lots. This purpose of this comparison is to vividly illustrate the power of exponential growth.
The key takeaway in this example is that the rate of increase in exponential growth can lead to dramatically larger results over time compared to linear growth, where the increase remains constant.
In the exponential scenario, the amount grows slowly at first but then increases at an astonishing rate, leading to a massive sum of $10,737,418.24 after just 31 days. In contrast, linear growth also leads to an increase, albeit with the total only reaching 31 cents after the same period.
To capitalize on the power of exponential growth within your business using my nine-step framework, I invite you to join my private Facebook group where I’ll share a video that makes every penny of this knowledge count. You can also reach me directly through Facebook. If you are not a Facebook member send me an email and request the YouTube video. Either way, remember, without putting this framework into action the potential for monumental financial growth remains just a collection of imagined cents and dollars, unearned. Turn theory into tangible profits. Watch the video.
