An electric current flowing in a circuit (consisting of a battery of $V$ volts and a resistor of $R$ ohms connected in series), satisfies

$$\frac{dI}{dt} = -k \left( I - b \right)$$

for some constants $k$ and $b$ with $k > 0$. Initially, $I(0) = 0$ and $I(t)$ approaches a maximum level $\frac{V}{R}$ as $t \to \infty$.

(a) What is the value of $b$?
$b =$

(b) Find a formula for $I(t)$ in terms of $k,\, V$, and $R$.
$I(t) =$

(c) What percent of its maximum value does $I(t)$ reach at time $t = \frac{3}{k}$?
%