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## Calculate Doubling in a Time Span

Calculator for the time for doubling and other duplications. Some things double regularly, this is called exponential growth. Here you can calculate if something doubles within a time span, how many times it multiplicates in another time span or how long it takes to reach a certain amount. Please enter a start amount and the time span for doubling. Below, enter either the end amount or the time for calculation.

Examples:

With a start value (amount 1) of 5 and an hourly doubling, after one hour 10 is reached, after 2 hours 20, after 7 hours 640. One hour before (-1 h), the amount was 2.5, at -2 hours it was 1.25. The amount 1 was at - 2 h 19 min 18,9 s.

Bacteria reproduce by cell division. Some bacteria do this every 20 minutes, then one bacterium becomes two. After 3 hours, 20 minutes, its number has multiplied by more than a thousand (1024 times). After one day, its number would have almost multiplied by 5 sextillions. This is only mathematically, in reality, growth has limits, which this calculator doesn't consider.

According to Moore's law, the number of transistors on an integrated circuit doubles approximately every 2 years (730.5 days) at the same cost. This law makes good predictions since the beginning of the 1990s, but it won't last forever.

The formula is:

z_{2} = z_{1} * log_{2}(a_{2}/a_{1})

a_{2} = a_{1} * 2^{z2/z1}

a_{1} = amount 1, a_{2} = amount 2, z_{1} = time 1 in seconds, z_{2} = time 2 in seconds

Since the values get very high very quickly when they are doubled frequently, reality will eventually present a hurdle that cannot be overcome. These are the natural limits mentioned above. In theory, the numbers are unlimited, but in practice the available material, space or money will eventually run out. But even before that, growth will slow down when you get closer to these limits.

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