Chapter 6.4, Problem 4DCYP

To determine

To find:whether it is reasonable to continue the trends.

Answer to Problem 4DCYP

It is not reasonable that if trends continue there will be no sales after $\text{15}$ year.

Explanation of Solution

Given:

  $\text{f}\left(\text{x}\right)\text{=-0}{\text{.17x}}^{\text{4}}\text{+6}{\text{.29x}}^{\text{3}}\text{-77}{\text{.65x}}^{\text{2}}\text{+251x+1100}$ .

Concept used:

The graph of the function $\text{f}$ is the set of all point in the plane of the form $\left(\text{x,f}\left(\text{x}\right)\right)$ .

The graph can be defined by the graph of $\text{f}$ and the equation for the graph will be $\text{y=f}\left(\text{x}\right)$ .

The tabular data of domain as $\text{x}$ and range $\text{y}$ while connecting the point to form curve which can be plot as graph using graphing calculator.

Calculation:

  $\text{f}\left(\text{x}\right)\text{=-0}{\text{.17x}}^{\text{4}}\text{+6}{\text{.29x}}^{\text{3}}\text{-77}{\text{.65x}}^{\text{2}}\text{+251x+1100}$ .

The graph of given function $\text{f}\left(\text{x}\right)\text{=-0}{\text{.17x}}^{\text{4}}\text{+6}{\text{.29x}}^{\text{3}}\text{-77}{\text{.65x}}^{\text{2}}\text{+251x+1100}$ is:

  

Hereturning point here is $\left(2.121,1339.628\right)$ and the curve is open down ward since the sign of the highest degree coefficient is negative and highest degree itself is even so, the end behavior is down and down.

The graph suggest that after $1990$ the annual sales in million dollar will be maximum after $\text{1992}\text{.121year}$ and the maximum amount will be $\text{1339}\text{.628}$ millions dollar after that the sales will reduced which can be seen from the graph that the slope reduce which means sales will reduce.

The sales of annual fax machine will be somewhat $\text{15}$ year after $\text{1990}$ will be $\text{0}$ .

Which mean there will be no sale after $\text{2005}$ .

Hence the trend will not continue after $\text{15}$ year.