When a camera flash goes off, the batteries immediately begin to recharge the flash's capacitor, which stores electric charge given by $q=q(t)=k(1-e^{-t/a})$.

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

(a) Find the inverse of this function. (Explain its meaning.)
(b) How long does it take to recharge the capacitor to $90$ percent of capacity if $a=2$?

(a) $t =$ \\ (b) $t =$ seconds [to the nearest tenth]