Chapter MPS, Problem 6.6MPS

(a)

To determine

To Draw: The graph of the given function.

Explanation of Solution

Given:

  $\begin{array}{l}w\left(n\right)=0.3n^3-0.4n^2+95\\ w=\text{Weight in pounds of the patient}\\ n=\text{Number of weeks since pateint became ill}\text{.}\end{array}$

Drawing:

  

(b)

To determine

To Explain: The end-behavior of the given function.

Explanation of Solution

Given:

  $\begin{array}{l}w\left(n\right)=0.3n^3-0.4n^2+95\\ w=\text{Weight in pounds of the patient}\\ n=\text{Number of weeks since pateint became ill}\text{.}\end{array}$

  

The given graph both ends are on the different side so it is odd-degree polynomials. And since the graph start down and go up so the function of the graph are positively leading coefficients.

(c)

To determine

To Explain: The trends in patient’s weight.

Explanation of Solution

Given:

  $\begin{array}{l}w\left(n\right)=0.3n^3-0.4n^2+95\\ w=\text{Weight in pounds of the patient}\\ n=\text{Number of weeks since pateint became ill}\text{.}\end{array}$

  

The given graph both ends are on the different side so it is odd-degree polynomials. And since the graph start down and go up so the function of the graph are positively leading coefficients. That’s why the trends in the patient’s weight suggest that it will increase in the long-term.