匿名使用者
匿名使用者 發問時間: 科學數學 · 1 0 年前

Average rate of change

A company producing computer components has established that on the average, a new employee can assemble N(t) components per day after t days of on-the-job training, as given by:

N(t)=40t/(t+2)

Find the average rate of change of N(t) from 3 days to 6 days

2 個解答

評分
  • 1 0 年前
    最佳解答

    Total no. of components assembled from 3 days to 6 days:

    ∫(t = 3 → 6) 40t/(t + 2) dt

    = ∫(t = 3 → 6) [40(t + 2)/(t + 2) - 80/(t + 2)] dt

    = ∫(t = 3 → 6) [40 - 80/(t + 2)] dt

    = [40t - 80 ln (t + 2)] (t = 3 → 6)

    = (240 - 80 ln 8) - (120 - 80 ln 5)

    = 120 - 80 ln 1.6

    So average no. of components assembled = 40 - (80 ln 1.6)/3

    And when t = 3, N(3) = 24 components per day

    When t = 6, N(6) = 30 components per day

    Hence average rate of change of N(t) = (30 - 24)/3 = 2

    參考資料: Myself
  • wy
    Lv 7
    1 0 年前

    N(3) = 40(3)/(3 + 2) = 40(3)/5 = 24.

    N(6) = 40(6)/(6 + 2) = 40(6)/8 = 30

    time taken = 6 - 3 = 3 days.

    so average components assembled = (30 - 24)/(6 - 3) = 6/3 = 2 per day.

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