"Cd" is the coefficient of drag (ie, how 'sticky' a given surface appears to the wind, a function of the object's shape and surface, or "form drag" and "surface friction") and is by definition a constant with respect to velocity, and thus does not change, not only within a range, but across all apparent wind speeds.

But the poster's math is correct (2x the speed = 2^2 = 4x the drag): the drag created by an object, of a given surface area and with a given Cd, increases with the square of the velocity (which as jbp notes is an exponent, but not "exponential").

For those that enjoy math and find it annoying hard work to increase their ground speed, the really harsh reality is that the power required to move an object through a viscous medium at a given speed is proportional to the speed times the drag. Since drag increases quadratically with velocity, required power increases with the cube of velocity (2x the speed = 4x the drag = 8x the power). Which is of course why the absolute speed differences between say a high level amateur and pro get small relative to their large differences in power output on a TT course, while their speed difference on a steep hill is enormous.