File:Special Duration Up Chart.png

Formulas
Inkzooka: 6.5*(1+(0.99*x-(0.09*x)^2)/55)

Bomb Rush: 6*(1+(0.99*x-(0.09*x)^2)/50)

Echolocator & Kraken & Bubbler: [base duration]*(1+(0.99*x-(0.09*x)^2)/75)

Base duration for all special weapons:
 * Echolocator: 12s
 * Inkzooka: 6.5s
 * Bomb Rush & Kraken: 6s
 * Bubbler: 5s
 * Killer Wail (attack time): 3s
 * Inkstrike (attack time): 1.5s