A company fits a model to the monthly sales data for a seasonal product. The model is

Chapter 4, Problem 64

(choose chapter or problem)

Average Sales A company fits a model to the monthly sales data for a seasonal product. The model is

\(S(t)=\frac{t}{4}+1.8+0.5 \sin \left(\frac{\pi t}{6}\right)\), \(0 \leq t \leq 24\)

where S is sales (in thousands) and t is time in months.

(a) Use a graphing utility to graph \(f(t)=0.5 \sin (\pi t / 6)\) 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.

Text Transcription:

f(t)=0.5 \sin (\pi t / 6)

S(t)=\frac{t}{4}+1.8+0.5 \sin \left(\frac{\pi t}{6}\right)

0 \leq t \leq 24