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14 December, 13:09

Yearly attendance at a local movie theater is 56,000 and grows continuously at a rate of 4.2% each year. What is the approximate attendance at the movie theater in nine years?

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  1. 14 December, 13:11
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    Yearly attendance = 56,000

    The growth rate is 4.2% or 0.042 per year.

    That is,

    Year 0: 56,000

    Year 1: 56,000*1.042

    Year 2: 56,000*1.042²

    and so on.

    This is a geometric sequence with

    a₁ = 56,000 and r = 1.042

    The n-th term is

    a (n) = a₁ rⁿ⁻¹

    When n=9, obain

    a₉ = 56,000*1.042⁸ = 77,826.9 ≈ 77,827

    Answer: 77,827
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