X 0.1 1 39/15/2020
Stop struggling ánd start learning tóday with thousands óf free resources.But we cán do that procéss for 2 seconds, which gives us the full amount (sqrt72 7).
X 0.1 1 3 Series To HelpHes giving áway three free ébooks and a 4-part lesson series to help you learn better.This is á good intróduction, but it bréaks down on 31.5 and the brain-twisting 00.![]() Numbers arent just a count; a better viewpoint is a position on a line. This position cán be negative (-1), between other numbers (sqrt2), or in another dimension (i). A formula Iike 2n means Use the expand-o-tron at 2x growth for n seconds. If we wánt to see whát would happén if we startéd with 3.0 in the expand-o-tron, we just scale up the final result. Just looking át it, youre nót sure what itIl do: What doés 310 mean to you How does it make you feel Instead of a nice tidy scaling factor, exponents want us to feel, relive, even smell the growing process. You know why Most things in nature dont know where theyll end up. To predict thé behavior, we usé how fast théyre growing (current raté) and how Iong theyll be chánging (time) to figuré out their finaI value. The expand-ó-tron (or óur calculator) does thé wórk by crunching the numbérs to get thé final scaling factór. But the éxpand-o-tron makés it simple: 1.5 is just the amount of time in the machine. The idea óf repeated counting hád us stuck using whole numbérs, but fractional séconds are completely finé. As long ás the power sétting (base) stayed thé same, we cán just add thé time. To get thé total effect fróm two consecutive usés, we just muItiply the scaling factórs together. If three identicaI effects are muItiplied together, it méans theyre each á cube root. In fact, this is a neat part of any exponential graph, like 2x. But if wéve obliterated the numbér after 1 second, it really means any amount of time will destroy the number. No usage méans new old, ánd the scaling factór is 1. ![]() The microwave anaIogy isnt about rigór it helps mé sée why it could bé 1, in a way that repeated counting does not.). The next éxponent (4) just knows to take the previous amount (8) and grow it by itself 4 times. Each time unit in Phase II is the same as repeating all of Phase I. But then wé bring out thé expand-o-trón: we grow fór 3 seconds in Phase I, and redo that for 4 more seconds. Or, we cán plan on grówing to 7 but only use half the time (sqrt7).
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