a tree height increases annually by 1/8 th of its height.by how much will its height increases after 2.5yr,if it stands today at 10m height ?
1/8 ---> .125
so height = 10(1.125)^2.5
= appr 13.4 m
To determine how much the height of the tree will increase after 2.5 years, we need to understand the rate at which the height increases annually.
Let's break it down:
The tree's height increases by 1/8th of its current height annually. So, each year, the tree's height increases by (1/8) * Current Height.
If the tree stands at 10 meters today, the height increase in the first year would be (1/8) * 10 = 1.25 meters.
After the first year, the tree's height would be 10 + 1.25 = 11.25 meters.
In the second year, the height would increase again by (1/8) * 11.25 = 1.40625 meters.
So, after two years, the tree's height would be 11.25 + 1.40625 = 12.65625 meters.
Finally, in the remaining 0.5 years, the height will increase again by (1/8) * 12.65625 = 1.582 meters.
Therefore, after 2.5 years, the tree's height will increase by a total of 1.25 + 1.40625 + 1.582 = 4.23825 meters.
Hence, the tree's height will increase by approximately 4.24 meters after 2.5 years.