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exponential growth
summary
the content delves into the patterns of exponential growth, focusing on how different bases affect the magnitude and direction of growth as exponents increase.
- exponential growth varies significantly with the base of the number, with positive bases greater than one growing larger at an accelerating rate.
- positive bases less than one result in values decreasing towards zero as the exponent increases, showcasing a diminishing pattern of growth.
- negative bases less than -1 exhibit an alternating pattern of growth, with absolute values increasing but alternating between positive and negative.
- negative fractions (bases between -1 and 0) also alternate between positive and negative, but their absolute values approach zero, indicating a diminishing pattern towards zero.
- the impact of increasing exponents on the magnitude of powers depends on the base, influencing whether powers get larger, smaller, or alternate in sign.
chapters
00:00
positive bases greater than one
01:54
positive bases less than one
03:04
negative bases less than -1
04:37
negative fractions
