A tree increases annually by $$\frac{1}{8}$$ of its height. By how much will it increase after $$2\frac{1}{2}$$ years if it stands today 8 m high ?

Solution(By Examveda Team)

Percentage annual increase
$$\eqalign{ & = \left( {\frac{1}{8} \times 100} \right)\% \cr & = \frac{{25}}{2}\% \cr} $$
Height after $$2\frac{1}{2}$$ years
$$\eqalign{ & = \left[ {8{{\left( {1 + \frac{{25}}{{2 \times 100}}} \right)}^2}\left( {1 + \frac{{25}}{{4 \times 100}}} \right)} \right]m \cr & = \left( {8 \times \frac{9}{8} \times \frac{9}{8} \times \frac{{17}}{{16}}} \right)m \cr & = \left( {\frac{{1377}}{{128}}} \right)m \cr & = 10.75\,\,m \cr} $$