Question 151691: I can't figure out where I went wrong, please help
104
worker efficiency In a study of worker efficiency at Wong Laboratories. it was found that the number of components assembled per hour by the average worker t hours after starting work could be modeled after the formula
N(t) = - 3t^2 + 23t^2 + 8t
a. rewrite the formula by factoring the right hand side completely.
b. Use the factored version of the formula to find N(3).
c. Use the graph to estimate the time at which the workers are most efficient.
d. Use the accompanying graph to estimate the maximum number of components assembled per hour during an 8 hour period.
a. -t (3t^2 - 24 t - 8 )
-t (3t + 1 )(t - 8)
b.
if t = 3
3N = -3 (3(3)+1)(3-8)
3N= -3(10)(-5)
3N= -3(-50)
3N= 150
N = 50
now the only problem i see is that according to the graph this
should be 5 not 50 can you tell what I have done wrong?
c. at 5 hours
d. estimate 235-240 components during the 5th hour
the total for the day is around 1275
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Well, you factoring is ok, except your initial formula is in error:
You wrote:
 but you did correct it later on by writing:
If you factor this, you get:
 which is precisely what you got!
Now you are asked to find N(3), so, setting t=3, we get...
You did err in this because you calculated 3*N, which was not asked for, and is not the same as N(3).
Now let's see what the graph of the given function  shows: (In the graph, N(t) is the vertical axis while t is the horizontal axis.
You can see that at t = 3, N(t) = 150.
And, at t = 5, N(t) = 240.
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