A tree increases annually by 1/8 th of its height. What will be its height after 2 years, if its height today is 64 cm?

Given, present height of the tree = 64 cm

The height of the tree increases by 1/8 th every year.

After 1st year

Height of tree = 64 + 1/8 of 64

⇒ Height of tree = 64 + 8 = 72 cm

After 2nd year

Height of tree = 72 + 1/8 of 72

⇒ Height of tree 72 + 9 = 81 cm

Another approach, it can be considered a CI problem:

Principal (initial height) = 64 cm, rate = 1/8 × 100 % = 12.5 %, t= 2 years, A= final height

For CI:

$(A = P{\left( {1 + \frac{r}{{100}}} \right)^t})$

Where,

A is the length at the end of time t,

P is the height at the starting of the time,

t is time in years.

r is growth rate in percent

⇒ Final height = $(64{\left( {1 + \frac{{12.5}}{{100}}} \right)^2})$

⇒ Final height = 64 × 1.1252

⇒ Final height = 64 × 1.265625 = 81 cm.