5Question: A science journalist tracks the growth of two plant species in a study. The height of Plant A after $ t $ weeks is modeled by $ h_A(t) = 2t + 3 $, and Plant B by $ h_B(t) = 3t + 1 $. After how many weeks will the plants have the same height? - Decision Point

Understanding the Context

To determine when both plants reach the same height, we set the two equations equal to each other:
$$ 2t + 3 = 3t + 1 $$

Now, solve for $ t $:
Subtract $ 2t $ from both sides:
$$ 3 = t + 1 $$
Then subtract 1:
$$ t = 2 $$

At $ t = 2 $ weeks, both plants have the same height. Substituting back to confirm:

• Plant A: $ h_A(2) = 2(2) + 3 = 4 + 3 = 7 $ cm
  
• Plant B: $ h_B(2) = 3(2) + 1 = 6 + 1 = 7 $ cm

Both models predict equal height after 2 weeks.

Key Insights

This simple calculation reveals valuable insight into relative growth rates: Plant B grows faster (slope = 3) than Plant A (slope = 2), so it outpaces the slower-growing Plant A, but only catches up at week 2 due to initial differences.

Understanding such growth milestones helps botanists, gardeners, and ecologists compare species performance, plan interventions, and predict ecosystem dynamics. Next time you observe plants in a garden or greenhouse, remember — behind every height, a story of time and math unfolds.

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Final Thoughts

Meta Description:
Explore how science tracks plant growth by comparing two models—Plant A (h_A(t) = 2t + 3) and Plant B (h_B(t) = 3t + 1). Learn when these species reach equal height and what it reveals about their growth rates. Perfect for students and nature enthusiasts.