• Build an exponential model from data.
• Build a logarithmic model from data.
• Build a logistic model from data.

Building Exponential Models From Data

A tech startup is tracking the growth of their mobile app downloads over the first 8 months after launch. The marketing team needs to predict future download patterns to plan their server capacity and advertising budget.

Month	Downloads (thousands)
1	12.5
2	18.7
3	28.1
4	42.3
5	63.8
6	96.2
7	145.1
8	218.6

In exponential growth, you’re looking for data that increases by multiplication rather than addition.

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Mathematical models are tools that work well within reasonable ranges, but real-world factors often create limits that pure exponential growth doesn’t account for. This is why models like logistic growth (which includes a limiting factor) are sometimes more realistic for long-term predictions.

Building Logarithmic Models From Data

As the startup gained more downloads, they focused on improving user experience based on feedback. They implemented the most requested features first, leading to big jumps in satisfaction. However, as they addressed major issues, remaining improvements became smaller and harder to achieve.

Month	Satisfaction Score (1-100)
1	45
2	62
3	71
4	76
5	79
6	82

Logarithmic growth starts fast but slows down over time.