Bellany planted a bush in his yard. At the time of planting the tree was three years old and measured 0.35 m in height. Bellany kept track of how the tree was growing over an eight year span and collected the data in the following table: 

Age of Tree (years)    Height (m) 

2                                   0.42 

4                                   1.55 

6                                   2.06 

8                                   2.51 

10                                   2.88 

12                                   3.03 

Determine the natural logarithm function in the form h(t) = a + bln(t) that models the tree, h(t), in meters, after time, t, in years. Round the a and b values to the nearest hundredth. How long will it take for the tree to be at least 6 m tall? Round your answer to the nearest year.