Answer:
(a). The initial rate is 2.60 A/s.
(b). The rate of current increases is 0.8658 A/s.
(c). The current is 0.435 A.
(d). The final steady-state current is 0.75 A.
Explanation:
Given that,
Inductance = 2.30 H
Resistance = 8.00 Ω
Voltage = 6.00 V
(a). We need to calculate the initial rate of increase of current in the circuit.
Using formula of initial rate


Put the value into the formula


The initial rate is 2.60 A/s.
(b). We need to calculate the rate of increase of current at the instant when the current is 0.500
Using formula of rate of increase of current
....(I)
Where, 


Using formula of current




The rate of current increases is
Put the value in the equation (I)


The rate of current increases is 0.8658 A/s.
(c). We need to calculate the current
Using formula of current

Put the value into the formula


The current is 0.435 A.
(d). We need to calculate the final steady-state current
Using formula of steady state



The final steady-state current is 0.75 A.
Hence, This is the required solution.