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exponential growth

mike mcgarry
lesson by mike mcgarry
magoosh expert
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