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, i

Question

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?​

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Thu Hương 4 years 2021-08-06T14:13:58+00:00 1 Answers 242 views 0

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  1. RuslanHeatt
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    2021-08-06T14:15:17+00:00
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    Answer: Approximately 2.29 cm

    Step-by-step explanation:

    • Week 1 = 1.67 or 1.67(1.04)^{0}
    • 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 = 1.67(1.04)^{x-1}

    Week 9 = 1.67(1.04)^{9-1} =1.67(1.04)^{8} =1.67(1.3686)=2.2855

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