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#1 2008-03-13 01:17:17

Identity
Member
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 big_smile

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#2 2008-03-13 02:48:27

JaneFairfax
Member
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
. big_smile

Last edited by JaneFairfax (2008-03-13 02:55:55)

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#3 2008-03-13 03:20:04

Identity
Member
Registered: 2007-04-18
Posts: 934

Re: Interesting exponential

Yep, well done Jane!

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