Growth Factor – Annual increase by one-eighth: A tree’s height increases each year by 1/8 of its current height (i.e., multiplied by 9/8 annually). If its present height is 64 cm, what will be the height after 2 years?

Introduction / Context:
This is a compound growth problem with multiplier 1 + 1/8 = 9/8 per year. Two years apply the multiplier twice.

Given Data / Assumptions:

• Present height H0 = 64 cm
• Annual multiplier = 9/8
• Years = 2

Concept / Approach:
Future height H = H0 * (9/8)^2.

Step-by-Step Solution:
(9/8)^2 = 81/64H = 64 * 81/64 = 81 cm

Verification / Alternative check:
Year 1: 64 * 9/8 = 72. Year 2: 72 * 9/8 = 81.

Why Other Options Are Wrong:
76, 80, 84 cm arise from simple (non-compound) additions or wrong multipliers.

Common Pitfalls:
Adding 1/8 of the original each year instead of 1/8 of the current height.

Final Answer:
81 cm