Exponential: Carbon-14 Half-life

Some things grow or decay in an exponential way. This means that for every time unit (e.g. a day) the metric changes with ± the same percentage. If you can say "it doubles every _ days" => this means it has exponential growth/increase! If you can say "it drops to half every _ days", it has logarithmic decay/decrease!

Growth calculation

Logarithmic decay

  • 2 → 1 = multiply by 0.50 (or -50.00 %) in 5730 year(s)
  • multiply by 0.988 (or -1.2 %) in 1 century
  • goes ÷ 2 every 57.26 century(s)
  • goes ÷ 5 every 132.96 century(s)
  • goes ÷ 10 every 190.22 century(s)
  • goes ÷ 100 every 380.44 century(s)

Extrapolation of data points

start point2.000 data point
after 14.32 century1.682interpolation
after 28.63 century1.414interpolation
after 42.95 century1.189interpolation
after 57.26 century1.000 data point
after 71.58 century0.841extrapolation
after 85.89 century0.707extrapolation
after 100.21 century0.595extrapolation
after 114.52 century0.500extrapolation
after 128.84 century0.420extrapolation
after 143.16 century0.354extrapolation
after 157.47 century0.297extrapolation
after 171.79 century0.250extrapolation
Created with Highcharts 11.1.0#Logarithmic decayLogarithmic decaystart pointafter 14.32​centuryafter 28.63​centuryafter 42.95​centuryafter 57.26​centuryafter 71.58​centuryafter 85.89​centuryafter 100.21​centuryafter 114.52​centuryafter 128.84​centuryafter 143.16​centuryafter 157.47​centuryafter 171.79​century0.20.40.60.8124

Examples

Carbon-14 has a radioactive half-life of 5730 years
Social Media: Facebook grew from 1 mio MAU in 2004 to 2.32 bil in 2018
Moore's Law: number of transistors on a chip doubles every 2 years (1990-2010)
Growth of people infected by COVID-19 in the USA between 15 and 29 March 2020
Business: month on month double digit growth = x 3.14 per year