Three years ago, a Sal tree was planted. The rate of its growth is 25% p.a. If the present height of the tree is 750 cm., what was its height when the tree was planted?

Question

anonymous · Answer

I hope this helps and is accurate,

Let's work backwards from the present height by taking 25% from it for each year for 3 years.

Currently it is 750cm, 25% of this or 0.25(750) is 187.5cm
If we subtract 187.5 from 750, we get 562.5
So a year ago the tree was 562.5cm

Let's go back one more year by taking 25% of this number and repeating the same idea.

0.25(562.5) =140.625cm, and subtracting from 562.5, we get 421.875cm

For the last year, we do the same, 0.25(421.875) = 105.46875, and subtracting, 421.875-105.46875 = 316.40625cm. 

So the tree should have been 316+/-0.5cm to start!

aum · Answer

Let x be the height of tree 3 years ago.
The rate of growth each year is 25%.
After 1 year, the height of the tree will be 1.25x
After 2 years, the height of the tree will be (1.25)^2x
After 3 years, the height of the tree will be (1.25)^3x

(1.25)^3x = 750
x = 750/(1.25)^3 = 384 cm.

anonymous · Answer

Wait, I was wrong then? Darn...

aum · Answer

If I start with 100 and increase it by 20% I get 120.
But if I take 20% off of 120 I won't get back 100.

So going backward will not work.