Growth by one-eighth annually — compute height after 2 years (Recovery-First applied): A tree increases annually by 1/8 of its height. If today it is 64 cm high, what will be its height after 2 years?

Introduction / Context:
(Recovery-First) The original stem asked “by how much will it increase,” but the options list final heights (e.g., 81 cm). To make the item solvable without changing its core meaning, we restate it to ask for height after 2 years, consistent with the options. Annual growth is a compound increase of 12.5% (1/8) each year.

Given Data / Assumptions:

• Initial height H0 = 64 cm
• Yearly growth rate = 1/8 = 12.5%
• Compounded annually for 2 years

Concept / Approach:
Height after n years: Hn = H0 * (1 + r)^n. Here, r = 1/8 so (1 + r) = 9/8. After 2 years, multiply by (9/8)^2.

Step-by-Step Solution:
H1 = 64 * (9/8) = 72 cmH2 = 72 * (9/8) = 81 cmHence the height after 2 years is 81 cm

Verification / Alternative check:
ΔH over 2 years = 81 − 64 = 17 cm. This is the “increase” the original stem likely intended, but since 17 cm is not an option, final height framing is appropriate.

Why Other Options Are Wrong:
72 cm is after 1 year only; 74 cm and 75 cm reflect incorrect additive growth; 80 cm undercounts the compound step.

Common Pitfalls:
Treating growth as linear (adding 1/8 of the original only once) rather than compounding year-on-year.

Final Answer:
81 cm