A botanist is studying the growth of a certain type of vine. The height of the vine, $h$, in inches, $w$ weeks after planting can be modeled by the equation $h=1.2w+5.5$, where $3\le w\le 15$. According to this model, what is the predicted height, in inches, of a vine 8 weeks after planting? Round your answer to the nearest tenth of an inch.