exponential growth
quiz
powers and roots
summary
the content delves into the patterns of exponential growth, focusing on how powers change with increasing exponents across different types of numerical bases.
- exponential growth varies significantly with the base value; a base greater than one grows rapidly with increasing powers.
- a positive base less than one results in decreasing values as the exponent rises, showcasing a pattern of rapid diminishment.
- negative bases less than -1 exhibit an alternating pattern of increasing absolute values, flipping between positive and negative.
- negative fractions (bases between -1 and 0) decrease towards zero, alternating between positive and negative values.
- the impact of increasing exponents on the power's size is contingent on the base's nature, influencing the answer to comparative questions about powers.
chapters
00:00
exponential growth with positive bases greater than one
01:53
diminishing values with positive bases less than one
03:04
alternating patterns with negative bases less than -1
04:35
approaching zero with negative fractions