A culture of bacteria grows according to the law N(t)=N0ekt, where N(t) is the number of bacteria present after t hours, N0 is the initial number, and k is a positive constant.
(i) Show that the time T required for the population to double satisfies T=kln2.
(ii) The culture initially contains 500 bacteria. After 3 hours the count is 800. Determine the value of k correct to four decimal places.
(iii) Using the value of k found in part (ii), calculate the time (to the nearest minute) at which the population will reach 2000.