Question 201851
Somehow you've got your independent variables a little muddled. I think that the independent variable is t (for time) and not r, as you have it!  So, let's start with...
{{{N(t) = -3t^3+23t^2+8t}}} and this represents the number of components assembled per hour by the average worker t hours after starting work.
A. The factored form is:
{{{N(t) = t(3t+1)(-t+8)}}}
B. Find {{{N(3)}}} using the factored form. Substitute t = 3.
{{{N(3) = 3(3(3)+1)(-3+8)}}} Evaluate.
{{{N(3) = 3(9+1)(5)}}}
{{{highlight(N(3) = 150)}}} Components per hour 3 hours after starting work.
The graph of {{{N(t)}}} is:
{{{graph(400,400,-5,10,-5,250,-3x^3+23x^2+8x)}}}
C. The estimated time, t, at which the workers are most efficient is t = 5, or 5 hours after starting work.
D. From the graph, it can be estimated that the maximum number of components assembled per hour during an eight-hour shift is 242.
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