Question

When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree was 1/5th taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year? a) 3/10 b) 2/5 c) 1/2 d) 2/3 e) 6/5

Answer 1

Option D is the correct answer.

Explanation:

Initial height = 4 feet

Given that the height of the tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree was 1/5th taller than it was at the end of the 4th year.

Let the rate of growing each year be g.

After 6 years height of tree = 4 + 6g

After 4 years height of tree = 4 + 4g

At the end of the 6th year, the tree was 1/5th taller than it was at the end of the 4th year.

That is

`4+6g=4+4g+(4+4g)/(5)\\\\4+6g=(20+20g+4+4g)/(5)\\\\20+30g=24+24g\\\\6g=4\\\\g=(2)/(3)ft/year`

Option D is the correct answer.