The random variable \(T\) is the lifetime, in hours, of a particular type of battery. It is given that \(T\) has a negative exponential distribution with mean 500 hours.
(i) Write down the probability density function of \(T\).

(ii) Find the probability that a randomly chosen battery of this type has a lifetime of more than 750 hours.

(iii) Find the median value of \(T\).