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#1 2008-03-13 01:17:17
- Identity
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- Registered: 2007-04-18
- Posts: 934
Interesting exponential
Without a calculator:
1.
Find the value of a such that
,touches but does not cross the line
.2.
What are the coordinates of the intersection of
, where a has been found in the previous question, and its inverse function?I think you will find the results are very elegant 
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#2 2008-03-13 02:48:27
- JaneFairfax
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- Registered: 2007-02-23
- Posts: 6,868
Re: Interesting exponential
If the curve touches the line at x[sub]0[/sub], then
and
Solve the two equations for a and x[sub]0[/sub]. a should be a value between 1.44 and 1.45 and x[sub]0[/sub] should be between 2.69 and 2.75.
Wait actually
and .
Last edited by JaneFairfax (2008-03-13 02:55:55)
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#3 2008-03-13 03:20:04
- Identity
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- Registered: 2007-04-18
- Posts: 934
Re: Interesting exponential
Yep, well done Jane!
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