The National Ignition Facility at the Lawrence Livermore National Laboratory maintains the world’s largest laser facility. The lasers, which are used to start a nuclear fusion reaction, are powered by a capacitor bank that stores a total of about 400 megajoules of energy. When the lasers are fired the capacitors discharge completely and then immediately begin recharging. The charge Q of the capacitors t seconds after the discharge is given by

Q(t) = Q₀(1 – e^–t/a)

(The maximum charge capacity is Q₀ and t is measured in seconds.)

(a) Find a formula for the inverse of this function and explain its meaning.

(b) How long does it take to recharge the capacitors to 90% of capacity if a = 50 ?