Coaxial cable Ethernet was limited to a maximum of $500$m between repeaters, which regenerate the signal to $100$% of its original amplitude. Along one $500$-m segment, the signal could decay to no less than $14$% of its original value $(8.5 dB)$. Along $1500$ m, then, the decay might be $(0.14)^{3} = 0.3$%. Such a signal, even along $2500$ m, is still strong enough to be read; why then are repeaters required every $500$ m?
