You can definitely grow hair in a week -- just not very much. Hair grows at a rate of 0.35 millimeters per day, so after seven days, your locks will be 2.45 millimeters -- or 0.01 inch -- longer. In a month, though, this adds up to about 1/4 inch of growth. You can't really do anything to speed up this rate, which is set according to your genetics and the natural hair growing cycle.
What You Can Do
Trim your hair regularly as it grows out to make sure it looks well-groomed and to avoid breakage. A healthy diet full of iron, biotin and zinc -- nutrients found in meats, nuts, seeds and whole grains -- also ensures hair health. A regular scalp massage as you shampoo will stimulate the hair follicles. Condition your hair regularly so that it stays healthy as it grows and looks as lustrous as you imagine when it reaches full length.