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This content has been automatically translated from Ukrainian.
Exponential growth is the process where a quantity increases in a geometric progression. In other words, each subsequent step multiplies the result several times from the previous one.
This type of growth is often encountered in computer algorithms, finance, or biology. For example, if the number of options doubles at each step, then after a few steps, there becomes an enormous amount that is difficult to process.
A simple Ruby code for demonstration:
# Exponential growth
base = 2 # multiplier
steps = 10 # number of steps
value = 1 # initial value
puts "Step - Value"
steps.times do |i|
puts "#{i + 1} - #{value}"
value *= base
end
The result will be:
Step - Value 1 - 1 2 - 2 3 - 4 4 - 8 5 - 16 6 - 32 7 - 64 8 - 128 9 - 256 10 - 512 => 10
This script shows how the initial value of 1 grows rapidly with a multiplier of 2. The result demonstrates why exponential growth quickly exceeds computable numbers.
Real-life examples:
- Technology: the number of transistors in processors grows according to Moore's law, approximately doubling every 2 years.
- Finance: compound interest, when investments grow exponentially due to interest compounding.
- Biology: the reproduction of bacteria in favorable conditions, where each bacterium divides into two after a certain period of time.
- Social networks: the spread of information or viral videos, where each user shares content with several friends.
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