Question

A tree increases annually by 1/8 of its height. By how much will it increase after 2½ years. If its length today is 8 m.?

Answer 1

The height of the tree today is 8 m.

The height of the tree increases by `(1/8)^"th"` of its height every year.

At the end of the 1^st year, the height of the tree will be

= `8 + 1/8 xx 8`

= 9 m

And, at the end of the 2^nd year, the height of the tree will be

= `9 + 1/8 xx 9 = 9(1 + 1/8)`

= `9 xx 9/8 = 81/8`

After six more months, the height of the tree will be = `81/8 + 1/16(81/8)`

= `81/8(1 + 1/16)`

= `81/8 xx 17/16`

= 10.75 m

∴ Increase in the height of the tree after `2^(1/2)` years = 10.75 – 8 = 2.75 m.