(a)

The equation is .

Where,  is maximum charge capacity.

Find the inverse of the function.

The function is .

Take natural logarithm on each side.

The inverse of the function is .

The inverse of the function gives the amount of time it takes for charge amount to reach .

(b)

Find the time to recharge the capacitor to 90% of capacity if .

Substitute   and  in .

Therefore, the time taken to recharge the capacitor to 90% of capacity if  is  seconds.

(a) The inverse of the function is .

The inverse of the function gives the amount of time it takes for charge amount to reach .

(b) The time taken to recharge the capacitor to 90% of capacity if  is  seconds.