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a plant grows by 1.67cm in its first week. each week it grows by 4% more than it did the week before. by how much will grow in nine weeks, including the first week?​

Respuesta :

jessmzhou4

Answer: Approximately 2.29 cm

Step-by-step explanation:

  • Week 1 = 1.67 or [tex]1.67(1.04)^{0}[/tex]
  • Week 2 = 1.67 + (1.67 · 4%) = 1.67 + 1.67 · 0.04 = 1.67(1 + 0.04) = 1.67(1.04)¹
  • Week 3 = 1.67(1.04) + [1.67(1.04) · 0.04] = 1.67(1.04)(1.04) = 1.67(1.04)²
  • Week 4 = 1.67(1.04)² + [1.67(1.04)² · 0.04] = 1.67(1.04)²(1.04) = 1.67(1.04)³

See a pattern?

  • Number of week = x
  • Plant growth = [tex]1.67(1.04)^{x-1}[/tex]

Week 9 = [tex]1.67(1.04)^{9-1} =1.67(1.04)^{8} =1.67(1.3686)=2.2855[/tex]

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