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 by the formula
N(t)=-3t+23t^2+8t
You did not post the question: the answers you are asked to find using that formula.
Here are questions to worker question solve the problem.
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 accompanying 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 shift.
300
*
200
100
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0 1 2 3 4 5 6 7 8
The production in components per hour at t hours after starting work
= N'(t)
= d(-3t+23t^2+8t)/dt
= -3+46t+8
= 5+46t
However, I believe there is a typo in the expression of N(t) where -3t...+8t does not appear right.
To determine worker efficiency at Wong Laboratories, the given formula N(t) = -3t + 23t^2 + 8t is used. In this formula, N(t) represents the number of components assembled per hour by the average worker t hours after starting work.
To calculate the worker efficiency at a specific time, you need to substitute the value of t into the formula N(t) and solve for N(t).
For example, to find the worker efficiency 2 hours after starting work (t = 2):
N(2) = -3(2) + 23(2)^2 + 8(2)
N(2) = -6 + 23(4) + 16
N(2) = -6 + 92 + 16
N(2) = 102
Therefore, the worker would assemble 102 components per hour after 2 hours of work.
This formula can be used for any time (t) value to determine the worker efficiency at that point in time.