Everything is supposedly growing exponentially these days. But when most people say “exponential,” they don’t mean what they say. They mean “fast.” **Exponential growth can indeed be fast. Or it can be slow. Excruciatingly slow.**

If you earn a million dollars a day, your wealth is growing quickly, but* not* exponentially. And if you have $100 in the bank earning 3% compound interest, your money is growing slowly, but it *is* growing exponentially.

Linear growth is a constant *amount* of increase per unit of time. Exponential growth is a constant *percentage* increase per unit of time. If you buy a pack of baseball cards every Friday, the size of your baseball card collection will grow linearly. But if you breed rabbits with no restriction, the size of your bunny heard will grow exponentially.

It matters a great deal whether you’re growing linearly or exponentially.

When you start a new enterprise — a company, a web site, etc. — it may truly grow exponentially. Growth may be determined by word of mouth, which is exponential (at first). The number of new people who hear each month depends on the number people who talk, and hearers become talkers. But that process can be infuriatingly slow when it’s just getting started. If the number of visitors to your web site is growing 5% per month, that’s great in the long term, but disappointing at first when it means going from 40 visitors one month to 42 the next.

**How do you live on an exponential curve? **You need extraordinary patience. While any exponential curve will eventually pass any linear curve, it may take a long time. If you’re making barely perceptible but compounding progress, be encouraged that you’re on the right curve. Eventually you’ll have all the growth you can handle. Realize that you may be having a harder time initially because you’re on the exponential curve rather than the linear curve.

**How do you know whether you’re on an exponential curve?** This is not as easy as it sounds. Because of random noise, it may be hard to tell from a small amount of data whether growth is linear or exponential, or even to tell growth from stagnation. Eventually the numbers will tell you. But until enough data come in to reveal what’s going on, look at the root causes of your growth. If you’re growing because customers are referring customers, that’s a recipe for exponential growth. If you’re growing because you’re working more hours, that’s linear growth.

**Nothing grows exponentially forever**. Word of mouth slows down when the message reaches saturation, when the talkers run into fewer people who haven’t heard. Rabbit farms slow down when they can’t feed all the rabbits. Most of the things we call exponential growth are more accurately logistic growth: exponential growth slows to linear growth, then linear growth begins to plateau.

**How do you live on a logistic curve? **Realize that initial exponential growth doesn’t last. Watch the numbers. They’ll tell you when you’ve gone from approximately exponential to approximately linear. Understand the mechanisms that turn exponential into logic growth in your context.

“Nothing grows exponentially forever” – except the economy of course ;)

Hi. Thanks for good explanation. Would appreciate a lot if you can explain exponential and logaritmic functions with examples , graph and usage.

Thanks.