Sorry, only got to reply now:

There was yet another small mistake in my equation, final version now:
camera.x += (target.x - camera.x) * pow(1 - reductionpersecond,time_step/16)

I simulated three different timesteps with both methods. Mine gives the exact same results for all timesteps, but I guess it may be slower because of the use of pow. Yours has small precision errors but I'm not sure if they have importance at any scale. I think it will ultimately depend on the situation.



Please let me know what you think.