The rate of increase of sales at the start of the second week ( t = 1 ) if the sales of OHaganBooks.com fits the cubic curve w ( t ) = − 3.7 t 3 + 74.6 t 2 + 135.5 t + 6 , 300 ( 0 ≤ t ≤ 6 ) to its weekly sales in the graph where t is a time in weeks.
The rate of increase of sales at the start of the second week ( t = 1 ) if the sales of OHaganBooks.com fits the cubic curve w ( t ) = − 3.7 t 3 + 74.6 t 2 + 135.5 t + 6 , 300 ( 0 ≤ t ≤ 6 ) to its weekly sales in the graph where t is a time in weeks.
Solution Summary: The author calculates the rate of increase of sales at the start of the second week if the sales of OHaganBooks.com fits the cubic curve.
To calculate: The rate of increase of sales at the start of the second week (t=1) if the sales of OHaganBooks.com fits the cubic curve w(t)=−3.7t3+74.6t2+135.5t+6,300(0≤t≤6) to its weekly sales in the graph where t is a time in weeks.
(b)
To determine
To calculate: The rate of increase of weekly sales at the start of the eighth week (t=7) if the model sales of OHaganBooks.com fits the cubic curve w(t)=−3.7t3+74.6t2+135.5t+6,300(0≤t≤6) to its weekly sales in the graph is extrapolated where t is a time in weeks.
(c)
To determine
To graph: The sketch of the function w for (0≤t≤20) and determine whether sales through week 20 can be predicted using the function where the sales of OHaganBooks.com fits the cubic curve w(t)=−3.7t3+74.6t2+135.5t+6,300(0≤t≤6) to its weekly sales in the graph is extrapolated where t is a time in weeks.
(d)
To determine
The reason for the quadratic model can predict radically different long term sales by comparing the graph fits the cubic curve.
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