Period of a REAL exponential function?

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So I don't exactly need my question to be solved for me, I just want to be pointed in the right direction. I need to determine the Fourier coefficients of a function $f(c) = {e}^{-cx}$, where $c$ is any arbitrary constant, in an interval $[0,1]$. If I'm suppose to be using a Fourier series for this, graphing $e^{cx}$ doesn't show some sort of period?

Am I lacking an understanding of the Fourier analysis or am I approaching the problem incorrectly?

Thanks for any help!