April 17, 2021

# Multiplying by two

Until now, Bitcoin has shown exponential growth in every halving cycle. Nobody complains about it. But the fact is that most people haveDifficulty understanding what exponential growth means. So here's another way to look at it: How long does it take for the value of Bitcoin to double?

Last year, after the 3rd halving, I wondered: what if the 3rd halving is played out according to the same scenario as the previous ones?

To project this situation, you just needtake the bitcoin price at the time of the 3rd halving and apply the growth trajectories in previous cycles to this value. This results in a blue range in the chart below. The orange curve on it is the actual trajectory of the BTC price in this new cycle.

For comparison, I also added a curve to the graphaverage growth trajectory. Let me emphasize that there is no particular reason to expect this cycle to be average compared to the previous ones. This line has been added for clarity purposes only, as it is difficult to visualize the arithmetic mean on a logarithmic graph.

Now that this point is clear, let me turn to a common comment I am used to hearing about this graph. It goes something like this:

“BTC is now worth about \$ 60K, and your chart predicts \$ 100K by April 18th. It is impossible for BTC to double in just a few weeks. "

First, this graph does not predict thatBitcoin will hit \$ 100k on April 18th. It simply shows that this will happen if the BTC price follows the average growth trajectory in previous halving cycles. Today it looks more like the market is following the middle of the range, which is the log average. We'll see.

Secondly, I, in general, will not be particularly surprised if BTC grows from 60 to 100 thousand dollars in two weeks. Why? Because this has happened in the past.

Here's one way to look at it.Start counting from any of the previous halvings and look at the bull market that followed. How long did it take for the price of bitcoin to double? And after that, how long did it take to double again? Once again?

After the first halving, the first doubling took about 77 days, the second took 35 days, the third 15 days, then 217 days, and finally 12 days for the fifth. Take a look for yourself:

So yes, with exponential growth, things can go pretty fast. A two-fold rise in prices within a halving cycle can take from a couple of weeks to several months.

In the current cycle, the first doubling took 6 months.The second is less than 2 months. As of today, we expect the next doubling in about 3 months; his goal is \$ 74 thousand. But this is what you get, starting from the moment of halving. To really understand what to expect, it's best to ask another question.

Let's take the price on any of the days. How long does it take to double the price from this point?

One way to answer this question is to look back and see:

• How often did the price double after 1 day?
• How often did the price double in 2 days?
• ...
• How often did the price double after 100 days?

And so on.

You can visualize this as a density plot.The horizontal axis shows how long you need to wait for the Bitcoin price to double. The higher the graph becomes, the more often this happens. The darker it gets, the closer to the average time before the price doubles. Take a look for yourself:

On average, the expectation of a twofold increase in the priceBitcoin takes about a year. But during a bull market, this can happen much faster. The large spike on the left side of the chart indicates that very often you only need to wait two months to double your money.

The picture as a whole suggests that there are tworegime. The range from 10 days to a year on the left side of the chart is most likely what you can expect when buying lows formed during a bear market or during the first phase of a bull market after a halving. A waiting time of more than a year is what you get when you buy at the late stage of the halving cycle.

That is, if this cycle is similar to the previous ones - andwhile it is, yes - at the current stage, you can still expect a two-fold increase in the price of bitcoin within a few weeks or months. So don't underestimate the likelihood that BTC will hit \$ 286k this fall.

The article does not contain investment recommendations,all the opinions expressed express exclusively the personal opinions of the author and the respondents. Any activity related to investing and trading in the markets carries risks. Make your own decisions responsibly and independently.

</p>