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exponential growth
summary
the content delves into the patterns of exponential growth, highlighting how the size of powers changes with increasing exponents across different types of bases.
- exponential growth varies significantly based on the base value, with distinct patterns for bases greater than one, less than one, negative bases less than negative one, and negative fractions.
- for a positive base greater than one, powers increase rapidly, becoming inconceivably large with higher exponents.
- a positive base less than one results in powers decreasing rapidly, approaching zero as exponents increase.
- negative bases less than negative one exhibit an alternating pattern of exponential growth, with absolute values increasing but alternating between positive and negative.
- negative fractions (bases between zero and negative one) also show an alternating pattern, but the absolute values decrease, approaching zero in a zig-zag manner above and below the zero line.
- the impact of increasing exponents on the size of powers depends on the base's value, with specific patterns for different base categories.
chapters
00:00
positive bases greater than one
01:54
positive bases less than one
03:03
negative bases less than negative one
04:37
negative fractions
