Algebra 2

Orlando is making a design for a logo. He begins with a square measuring 20 inches on each side. The second square has a side length of 16 inches, and the third square has a side length of 12.8 inches. Which square will be the first square with a side length of less than 8 inches?

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  1. I'm thinking the sixth square..........

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  2. looks like each side is 4/5 of its previous , so

    20(4/5)^n = 8
    (.8)^(n-1) = .4
    using logs
    (n-1) log .8 = log .4
    n - 1 = 4.1
    n = 5.1
    so the 5th would be less than 8
    and the 6th would be greater than 8

    e.g.

    1st --- 20
    2nd -- 16
    3rd -- 12.8
    4th -- 10.24
    5th -- 8.192
    6th -- 6.5536

    You were right, how did you reason it ?

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