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13 August, 02:46

5. The value of a sculpture is increasing 5% every month. The original value of the

sculpture is $6400. Identify the exponential growth function to model this situation.

Then find the value of the sculpture after 30 months.

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Answers (1)
  1. 13 August, 02:54
    0
    The expression that represents the value of the sculpture by month is:

    value (n) = value (0) * 1.05^n

    And the value after 30 months is:

    $27660.431

    Step-by-step explanation:

    If the value of the sculpture is increasing 5% every month, then initially it's value will be:

    value (0) = 6400

    After the first month:

    value (1) = value (0) * 1.05

    After the second month:

    value (2) = value (1) * 1.05 = value (0) * 1.05*1.05 = value (0) * (1.05^2)

    After the third month:

    value (3) = value (2) * 1.05 = value (0) * (1.05^2) * 1.05 = value (0) * (1.05^3)

    Therefore the equation that can model this growth is:

    value (n) = value (0) * 1.05^n

    After 30 months it'll be:

    value (30) = 6400*1.05^ (30) = 27660.431
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