Chapter 6.6, Problem 28PPS

a.

To determine

To calculate: the sales for 2010 and 2015.

Answer to Problem 28PPS

In 2010, there will be about $1047$ sales in millions of dollars and in 2015 , there will about $1042$ sales in millions of dollars.

Explanation of Solution

Given information:

A company’s sales , in millions of dollars , of consumer electronics can be modeled by $S(x)=-1.7x^3+18x^2+26.4x+678$ where x is the number of years since 2005.

Formula used:

Synthetic Substitution :- Synthetic division is used to find the value of a function.

Calculation:

Consider ,

  $S(x)=-1.7x^3+18x^2+26.4x+678$

By using Synthetic substitution the function is supposed to divided by $x-5\text{ and }x-10$ respectively.

Therefore, we have

  $\begin{array}{l}\overline{)5}\begin{array}{cccc}-1.7& 18& 26.4& 678\end{array}\\ \begin{array}{ccc}-8.5& 47.5& 369.5\end{array}\\ \overline{\begin{array}{ccc}-1.7& 9.5& 73.9\end{array}\hspace{.2em}|}\text{ 1047}\text{.5}\end{array}$

  $\begin{array}{l}\overline{)10}\begin{array}{cccc}-1.7& 18& 26.4& 678\end{array}\\ \begin{array}{ccc}-17& 10& 364\end{array}\\ \overline{\begin{array}{ccc}-1.7& 1& 36.4\end{array}\hspace{.2em}|}\text{ 1042}\end{array}$

In 2010, there will be about $1047$ sales in millions of dollars and in 2015 , there will about $1042$ sales in millions of dollars.

b.

To determine

To explain: whether the model is useful or not. speed of the boat at 6 seconds.

Explanation of Solution

Given information:

A company’s sales , in millions of dollars , of consumer electronics can be modeled by $S(x)=-1.7x^3+18x^2+26.4x+678$ where x is the number of years since 2005.

Formula used:

Synthetic Substitution :- Synthetic division is used to find the value of a function.

Proof:

Synthetic Substitution is the method that help us to find the value of a function in more appropriate manner. This model is useful in estimating future sales.

The above part is a good example for this model.

Hence, the model is useful.