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Mathematics 12 Online
OpenStudy (darkbluechocobo):

Help with exponential fractions

OpenStudy (darkbluechocobo):

Let f(x) = e^x and gf(x) = 2^x . For all x > 0, f(x) > g(x).

OpenStudy (darkbluechocobo):

is this false?

OpenStudy (jdoe0001):

hmm what's \(\Large \bf e \ ?\) anyway?

OpenStudy (freckles):

does gf(x)=2^x?

OpenStudy (freckles):

or did you mean g(x)=2^x?

OpenStudy (noelgreco):

Check it with a fractional exponent.

OpenStudy (freckles):

and also joe asks a good question :) he is asking you what you think e is

OpenStudy (darkbluechocobo):

sorry i meant g(x) aha

OpenStudy (darkbluechocobo):

e ≈ 2.71828

OpenStudy (jdoe0001):

so... what do you think then... which value would be bigger for x > 0 \(\bf \large 2.71828^x\quad or\quad 2^x ?\)

OpenStudy (darkbluechocobo):

2.7^x

OpenStudy (jdoe0001):

yeap

OpenStudy (darkbluechocobo):

false then? since f(x)<g(x)

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