A tree grows 2.80 m during the first year since it was planted. During each subsequent year, the tree's growth is 85% of its growth the previous year. Determine the first year in which the growth of the tree is less than half a metre.
+128475 We need to solve this for n
2.8 ( .85)^(n - 1) = .5
(.85)^(n - 1) = .5/2.8
(.85)^(n - 1) = 5/28 take the log of both sides
log (.85(^(n - 1) = log (5/28) and by a log property we can wite
(n - 1) log (.85) = log (5/28)
n - 1 = log (5/28) /log (.85)
n = log (5/28) / log (.85) + 1 ≈ 11.6 yrs
So about the 12th year
