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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.?
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Solution
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 1st year, the height of the tree will be
= `8 + 1/8 xx 8`
= 9 m
And, at the end of the 2nd 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.
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