I keep messing with this two concepts
In: Mathematics
**Exponential growth:** every fixed amount of time, it doubles. Equivalently, exery fixed amount of time, it gains a zero. So, it’s superfast. So fast it’s impossible for anything to growth this fast for long.
*Example:* today 1, tomorrow 10, next day 100, next day 1,000, then 10,000, then 100,000…. After just another week: 1,000,000,000,000. And that’s still nothing compared to the next day.
**Logarithmic growth:** it increases by a fixed amount in some time, and then takes twice that time to increase as much again, then twice the time again for another step, and so on. Equivalently: to grow a fixed amount, it takes ten times what it took last time to grow just as much. So, it’s superslow. So slow it basically does not grow at all.
*Example:* today 1. Tomorrow, 2. In 10 more days: 3. In 100 days: 4. After 1000 days (3 years): 5. Then it takes 30 years to go up to 6. After another 300 years, it’s just 7, and 3 millennia later it’s 8, 30 millennia later it’s 9. If you waited another billion years, it would not have grown to 13 yet. After another 10 billions years the universe is over but you are still waiting for 14.
Simple explanation: an exponential function has an increasing slope i.e it gets steeper as the x value increases. A logarithmic function gets shallower i.e. the curve flattens out as x increases.
For a more nuanced explanation check out google and the images/videos there. They do a better job than I can in words.
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