So we started difference equations and im having a very very hard tome wrapping my head around it, im using our assigned textbook. How am I supposed to read 2^t(2)
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If you need a image for more context let me know – AnonGal Jan 16 '20 at 00:09
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6Yes, an image would help. – JohnD Jan 16 '20 at 00:11
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1the name of the textbook would also help. With authors, and edition number – Will Jagy Jan 16 '20 at 00:18
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"Mathematics for Economics" by Micheal Hoy, John Livernois, Chris McKenna, Ray Rees, Thanasis Stengo. Third Edition – AnonGal Jan 16 '20 at 00:34
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1Looks like when they write $2^t(2)$ they just mean $2^t\times 2$... – Jan 16 '20 at 00:35
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So how does that link 2^t = 2^(t+1)? I'm struggling to see the relation – AnonGal Jan 16 '20 at 00:38
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They are trying to verify that $y_t=2^t$ satisfies the difference equation. It indeed does, because $y_{t+1}=2^{t+1}=2\cdot 2^t=2y_t$. – Jan 16 '20 at 00:41
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They are not equal without the following factor of $2$. The paragraph is trying to justify that $2^t$ satisfies the recurrence. – Ross Millikan Jan 16 '20 at 00:41
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Quick question...wouldn't that make it 4yt? ...Apologies if my questions are beyond dumb but this topic is so jarring to me – AnonGal Jan 16 '20 at 00:46
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The text you show says "writing $2^{t+1}$ as $2^t(2)$", which clearly means that $2^{t+1}$ is the same as $2^t$ times $2$. In other words, multiplying $t+1$ copies of $2$ gives the same result as multiplying $t$ copies times one more copy of $2$. Right? – hardmath Jan 16 '20 at 05:18
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The whole sentence, which it would have helped a lot if you quoted it, says But $2^{t+1}=2^t(2)$. It is just multiplication, as in $2^{t+1}=2^t \cdot 2$
Ross Millikan
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They are simply saying that $2^{t+1}$ is the same as writing $ 2^{t}2$. Utilizing the exponent rules (don't know how it's really phrased in english) where $$a^{b+c} = a^{b}a^{c}.$$ Hope this helped you.
whoami
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