Question 208058
I am trying to find the domain of 
f(t)=4.5e^t

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You don't need to find the domain.  It is always
"All Real Numbers" unless there is some aspect of
the equation that excludes some of the Real Numbers.
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In your problem there is no such exclusion, so the
domain is All Real Numbers.
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If, however the problem includes some words which 
might indicate the "t" is time starting at zero,
then the domain would be "All Real Numbers >0 zero.
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Cheers,
Stan H.