Question

Mr, Blagrew planted a tree that doubles its height each year until it reaches its maximum height in six years. What fraction represents the height of the tree when it was planted?

Answer 1

The fraction representing the original height of the tree when it was planted is 1/64 of its maximum height. This is calculated using exponential growth in reverse, considering the tree doubles its height each year and reaches its maximum height in six years.

Step-by-step explanation:

The problem involves determining the original height of a tree bearing in mind that the tree doubles its height each year until it reaches its maximum height in six years. To solve this, we can use the concept of exponential growth in reverse. Since the tree doubles in height each year, we can express its height as a fraction of its maximum height at the end of six years. After one year, it would be ½ of the maximum height, after two years, ¼, and so on until (1/2)^6 of the maximum height when it was first planted.

To represent this as a fraction, the calculation would be (1/2)^6, which equals 1/64. Therefore, the fraction that represents the height of the tree when it was planted is 1/64 of its maximum height.