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? - 500apps

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.

Keywords: Plant growth comparison, height difference equation, linear growth model, science study analysis, when will plants be same height, science journalism, growth rate analysis, mathematical modeling in biology, 5Question plant growth problem, tracking plant species heights.

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.