Average Sales A company fits a model to the monthly sales data for a seasonal product. The model is s ( t ) = t 4 + 1.8 + 0.5 sin ( π t 6 ) , 0 ≤ t ≤ 24 where S is sales (in thousands) and t is time in months. (a) Use a graphing utility to graph f ( t ) = 0.5 sin( ( π t / 6 ) ) for 0 ≤ t ≤ 24. Use the graph to explain why the average value of f ( t ) is 0 over the interval. (b) Use a graphing utility to graph S ( t ) and the line g ( t ) = t / 4 + 1.8 in the same viewing window. Use the graph and the result of part (a) to explain why g is called the trend line.
Average Sales A company fits a model to the monthly sales data for a seasonal product. The model is s ( t ) = t 4 + 1.8 + 0.5 sin ( π t 6 ) , 0 ≤ t ≤ 24 where S is sales (in thousands) and t is time in months. (a) Use a graphing utility to graph f ( t ) = 0.5 sin( ( π t / 6 ) ) for 0 ≤ t ≤ 24. Use the graph to explain why the average value of f ( t ) is 0 over the interval. (b) Use a graphing utility to graph S ( t ) and the line g ( t ) = t / 4 + 1.8 in the same viewing window. Use the graph and the result of part (a) to explain why g is called the trend line.
Solution Summary: The author illustrates the graphing utility of f(t)=0.5mathrmsin(pi t6).
Average Sales A company fits a model to the monthly sales data for a seasonal product. The model is
s
(
t
)
=
t
4
+
1.8
+
0.5
sin
(
π
t
6
)
,
0
≤
t
≤
24
where S is sales (in thousands) and t is time in months.
(a) Use a graphing utility to graph
f
(
t
)
=
0.5
sin(
(
π
t
/
6
)
) for
0
≤
t
≤
24.
Use the graph to explain why the average value of
f
(
t
)
is 0 over the interval.
(b) Use a graphing utility to graph S(t) and the line g(t)
=
t
/
4
+
1.8
in the same viewing window. Use the graph and the result of part (a) to explain why g is called the trend line.
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