Chapter 11, Problem 57RE

(a)

To determine

To calculate: The rate of increase of sales at the start of the second week $\left(t=1\right)$ if the sales of OHaganBooks.com fits the cubic curve $w\left(t\right)=-3.7t^3+74.6t^2+135.5t+6,300\left(0\le t\le 6\right)$ 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 $\left(t=7\right)$ if the model sales of OHaganBooks.com fits the cubic curve $w\left(t\right)=-3.7t^3+74.6t^2+135.5t+6,300\left(0\le t\le 6\right)$ 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 $\left(0\le t\le 20\right)$ and determine whether sales through week $20$ can be predicted using the function where the sales of OHaganBooks.com fits the cubic curve $w\left(t\right)=-3.7t^3+74.6t^2+135.5t+6,300\left(0\le t\le 6\right)$ 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.