No, that is just plain wrong. All attenuation is exponential (except very special stuff like energy resonances at certain particle energies). You just get very different exponents for rarely vs. frequently interacting particles. The charge of an alpha particle is also only twice the charge of a beta particle with a far higher (orders of magnitude, not just a factor of 2) penetration depth. The relevant difference is actually the mass and size (i.e. cross-section) of an alpha particle that makes it far more frequently interacting.

There are some more differences that govern the cross-section like conservation of momentum and angular momentum in certain interactions where there are differences between gamma and alpha particles. Or magic number nuclei that are relevant for neutron absorption.

But in general, for a given material and particle, attenuation is always always always exponential over the penetration depth vs number of particles, until you hit a low enough energy that some other mechanism for energy transfer can come into play or become unavailable, where the exponent will change and you will see a change in slope.