The tread of a car tyre wears more rapidly as it becomes thinner. The tread-wear rate, measured in mm per 10 000 miles, may be modelled as  a + b(d – t)² where d is the initial tread depth, t is the current tread depth and a and b are constants. A tyre company takes measurements on a new design of tyre whose initial tread depth is 8 mm. When the tyre is new its wear rate is found to be 1.03mm per 10 000 miles run and when the tread depth is reduced to 4mm the wear rate is 3.43mm per 10 000 miles. Assuming that a tyre is discarded when the tread depth has been reduced to 2 mm, what is its estimated life?