When a camera flash goes off, the batteries immediately begin to recharge the flash

$Q(t)=Q_0(1-e^{-\frac{t}{a}})$

where $Q_0$ is the maximum charge and $t$ is measured in seconds since the flash went

$($a$)$ Find the inverse of the function $Q^{-1}.$

$t(Q)=$

$$

Explain its meaning in the context of this problem.

This gives us the charge $Q$ obtained within a given time $t.$

This gives us the time $t$ with respect to the maximum charge capacity $Q_0$

This gives us the time $t$ necessary to obtain a given charge $Q.$

$($b$)$ How long does it take to recharge the capacitor to $95\%$ of capacity if $a=77(1$

$$ sec