Chapter 1.5, Problem 90E

a.

To determine

Plot the graph in the same viewing window.

Answer to Problem 90E

  

Explanation of Solution

Calculation:

Consider the below table

  $\begin{array}{cc}Time,x& Temperature,y\\ 0& 34\\ 2& 50\\ 4& 60\\ 6& 64\\ 8& 63\\ 10& 59\\ 12& 53\\ 14& 46\\ 16& 40\\ 18& 36\\ 20& 34\\ 22& 37\\ 24& 45\end{array}$

Use the T1-83 to enter the table as shown in below steps

Click on the “stat” button

  

Select “edit” by clicking on 1 then below screen will appear

  

Enter the table values under $L1$ and $L2$ or enter the values under $x$ and $y$ by creating them as

  

Click on 2^nd button and “stat plot” button in T1-83 calculator then below screen will appear

  

Select the Plot 1 and choose plot type as shown below

  

Click on “window” button and set the minimum and maximum values of labels (axis)

  

Click on the graph then below screen will obtain

  

Consider the equation

  $y=0.026x^3-1.03x^2+10.2x+34$

Enter the equtaion in $T1-83$ by clicking on $"y="$ button

  

Click on the graph the below screen will obtain

  

b.

To determine

Verify that the model fit the data.

Answer to Problem 90E

  

Explanation of Solution

Calculation:

Consider the below table

  $\begin{array}{cc}Time,x& Temperature,y\\ 0& 34\\ 2& 50\\ 4& 60\\ 6& 64\\ 8& 63\\ 10& 59\\ 12& 53\\ 14& 46\\ 16& 40\\ 18& 36\\ 20& 34\\ 22& 37\\ 24& 45\end{array}$

Hence, the equation exactly set the data as shown in the below graph in $T1-83$ calculator

  

c.

To determine

Use the graph to approximate the times when the temperature was increasing and decreasing.

Answer to Problem 90E

The temperature was increasing for the first $8$ hours and decreasing after that.

Explanation of Solution

Calculation:

Consider the below table

  $\begin{array}{cc}Time,x& Temperature,y\\ 0& 34\\ 2& 50\\ 4& 60\\ 6& 64\\ 8& 63\\ 10& 59\\ 12& 53\\ 14& 46\\ 16& 40\\ 18& 36\\ 20& 34\\ 22& 37\\ 24& 45\end{array}$

  

Hence, the temperature was increasing for the first $8$ hours and decreasing after that .

d.

To determine

Use the graph to approximate the maximum and minimum temperatures during this $24$ -hour period.

Answer to Problem 90E

  

  

Explanation of Solution

Calculation:

Consider the below table

  $\begin{array}{cc}Time,x& Temperature,y\\ 0& 34\\ 2& 50\\ 4& 60\\ 6& 64\\ 8& 63\\ 10& 59\\ 12& 53\\ 14& 46\\ 16& 40\\ 18& 36\\ 20& 34\\ 22& 37\\ 24& 45\end{array}$

Hence, the maximum temperature is after $6$ hours and minimum after $20$ hours as shown below

  

  

e.

To determine

Could this model predict the temperatures in the city during the next $24$ -hour period?

Answer to Problem 90E

The model cannot be used to predict the future because for the next $24$ hours also the same temperature will obtain.

Explanation of Solution

Calculation:

Consider the below table

  $\begin{array}{cc}Time,x& Temperature,y\\ 0& 34\\ 2& 50\\ 4& 60\\ 6& 64\\ 8& 63\\ 10& 59\\ 12& 53\\ 14& 46\\ 16& 40\\ 18& 36\\ 20& 34\\ 22& 37\\ 24& 45\end{array}$

Hence, the model cannot be used to predict the future because for the next $24$ hours also the same temperature will obtain.