What would be a good equation to smoothly connect these two line segments? ($y=1$ and $y=c^{-x}$)

Question

I am trying to build a smoothed decay envelope.

If I have a signal starting a $y=1$, and want it to transition to $y=c^{-x}$, what would be simple/effective for doing this mathematically in the space between?

For example: https://www.desmos.com/calculator/frsrrd0ad3

This is for smoothing the decays of audio signals, so in principle, there should be no sharp edges or discontinuities. It should be the simplest, most natural, smooth line for which there are no obvious points or corners.

Thanks.