Chapter 1.9, Problem 3MRPS

Solution

a.

To graph: The price of the part versus time.

The required graph is draw as follows,

  

Given Information:

The table is draw as,

x	y
0	133
1	102
2	81
3	71
4	61
5	61

Explanation:

Consider the given table,

Draw the given table on the coordinate plane to draw the graph.

The obtained graph is as follows,

  

b.

To determine: The shape of the graph and find the equation to model the graph as part (a).

The shape of the graph is quadratic, and the required model is $y=3.5536x^2-31.854x+131.89$ .

Explanation:

As it can be observed form the graph of part (a), the given points are making a quadratic equation graph on the coordinate plane.

Use the following steps to find the graph.

Step 1. Insert the data in the excel as,

  

Step 2. Select the table, Click on the “Insert” option and go to the chart.

  

Step 3. Click on the “First Scatter option”.

After click on the scatter plot the obtained graph is as followed.

  

Step 4. Click on the “Plus sign”, select the trend line and click on more options.

  

Step 5. After click on the more option, select the polynomial, which have already second degree.

  

Step 5. Click on the “Display equation on chart” option.

  

Thus, the obtained graph and equation by using excel is as follows.

  

Therefore, the shape is quadratic, and the required equation of model is $y=3.5536x^2-31.854x+131.89$ .

c.

To calculate: The estimation by using the model in 2015 and explain it correct or not.

The obtained estimation is $\$83$ and this is the correct estimation.

Calculation:

Consider the obtained model,

  $y=3.5536x^2-31.854x+131.89$

Substitute 7 for $x$ in the above model.

  $\begin{array}{c}y=3.5536{\left(7\right)}^2-31.854\left(7\right)+131.89\\ =\text{174}\text{.1264}-\text{222}\text{.978}+131.89\\ \approx \$83\end{array}$

Now, draw the point $\left(7,83\right)$ on the same coordinate as given table drawn.

  

As it can be observed that the obtained point also performing the shape of the quadratic equation. Thus, this is the correct estimation.

Therefore, the obtained estimation is $\$83$ and this is the correct estimation.