Beginning from April of a year, the rate of which a tree became taller increased linearly for 15 weeks when it was trimmed down. From then on, the rate decreased linearly for the next 15 weeks.

Which graph correctly shows the height of the tree against time during this period?

Correct option is A

Solution:

The problem describes how a tree's height changes over 30 weeks:

1. First 15 weeks:

   • The growth rate increases linearly, meaning the tree grows at an accelerating pace.
   • This suggests a curved upward pattern in the graph.

2. At the 15th week:

   • The tree is trimmed down, causing a sudden drop in height.

3. After trimming (next 15 weeks):

   • The tree continues growing, but the growth rate again increases linearly, meaning it starts slow and picks up speed gradually.

Step-by-Step Analysis of the Graphs:

• Graph (A):

  • First 15 weeks: Shows accelerating growth (curved upward).
  • At 15 weeks: A sudden drop in height due to trimming.
  • Next 15 weeks: Growth resumes with an increasing rate (curved upward).
  • Correct representation of the tree’s growth.

• Graph (B):

  • Shows a steady growth rate after trimming, but does not show an increasing rate afterward.

• Graph (C):

  • Shows the correct initial acceleration and trimming, but the second phase does not show accelerating growth correctly.

• Graph (D):

  • Shows a decreasing growth rate after trimming, which is incorrect.

Final Answer: (a) A