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
Average rate of change
2009-12-11 11:15 pm
回答 (2)
2009-12-11 11:31 pm
✔ 最佳答案
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: Myself
2009-12-12 2:45 am
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.
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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