HOW DO YOU SEE IT? The cost C (In dollars) of producing x units of a product is C = 60 x + 1350. For one week, management determined that the number of units produced x at the end of t hours was x = − 1.6 t 3 + 19 t 2 − 0.5 t − 1 . The graph shows the cost C in terms of the time t . Using the graph, which is greater, the rate of change of the cost after 1 hour or the rate of change of the cost after 4 hours? Explain why the cost function is not increasing at a constant rate during the eight-hour shift.
HOW DO YOU SEE IT? The cost C (In dollars) of producing x units of a product is C = 60 x + 1350. For one week, management determined that the number of units produced x at the end of t hours was x = − 1.6 t 3 + 19 t 2 − 0.5 t − 1 . The graph shows the cost C in terms of the time t . Using the graph, which is greater, the rate of change of the cost after 1 hour or the rate of change of the cost after 4 hours? Explain why the cost function is not increasing at a constant rate during the eight-hour shift.
Solution Summary: The author analyzes the rate of change of cost after 1 hour or after 4 hours using the graph.
HOW DO YOU SEE IT? The cost C (In dollars) of producing x units of a product is C = 60x + 1350. For one week, management determined that the number of units produced x at the end of t hours was
x
=
−
1.6
t
3
+
19
t
2
−
0.5
t
−
1
. The graph shows the cost C in terms of the time t.
Using the graph, which is greater, the rate of change of the cost after 1 hour or the rate of change of the cost after 4 hours?
Explain why the cost function is not increasing at a constant rate during the eight-hour shift.
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