Chapter 1.10, Problem 71E

(a)

To determine

The scatter plot of the data.

Answer to Problem 71E

The value gets decreases continuously based on the temperature and depth.

Explanation of Solution

Given information:

The ordered pairs are given with the average water temperature C in degree Celsius at several depths d in meters in the Indian Ocean.

  

Formula used:

The depth in meters is plotted against the x-axis and the temperature is plotted in y-axis.

Calculation:

With the help given data sketch a scatter plot by using graph utility:

  

  $T=\frac{k}{d}$

Conclusion:

The value gets decreases continuously based on the temperature and depth.

(b)

To determine

The direct variation model or an inverse variation model better fits the data.

Answer to Problem 71E

The value of model get increases continuously.

Explanation of Solution

Given information:

The ordered pairs are given with the average water temperature C in degree Celsius at several depths d in meters in the Indian Ocean.

  

Formula used:

  

Calculation:

Yes, the data appears to be modelled by the inverse proportion model.

  

Conclusion:

The value of model $T=\frac{k}{d}$ gets increases continuously.

(c)

To determine

The value of $k$ for each pair of coordinates.

Answer to Problem 71E

The value of is $k=4920$ . Therefore, the model $T=\frac{4920}{d}$

Explanation of Solution

Given information:

The ordered pairs are given with the average water temperature C in degree Celsius at several depths d in meters in the Indian Ocean.

  

Formula used:

  $\text{Mean = }\frac{\text{Sum}\text{of}\text{values}}{\text{Total}\text{number}}$

Calculation:

The mean value of k will be

Mean,

  $\begin{array}{l}k=\frac{4850+5287.5+4936+4720+4749+4977}{6}\\ k=4920\end{array}$

Thus, the value of is $k=4920$ . Therefore, the model $T=\frac{4920}{d}$

Conclusion:

The value of is $k=4920$ . Therefore, the model $T=\frac{4920}{d}$

(d)

To determine

The model for the depth at which the water temperature is $3^{\circ }C$

Answer to Problem 71E

The approximate the depth is at 1640 meters at which the water temperature is 3°C.

Explanation of Solution

Given information:

The ordered pairs are given with the average water temperature C in degree Celsius at several depths d in meters in the Indian Ocean.

  

Formula used:

  

Calculation:

Use the model derived in part $\left(c\right)$ and substituting the value $T=3$ into the model,

  $\begin{array}{l}T=\frac{4920}{d}\text{the inverse variation}\\ 3=\frac{4920}{d}\text{Substitute the values}\\ d=1640\text{Simplify}\end{array}$

Thus, the approximate the depth is at 1640 meters at which the water temperature is 3°C.

Conclusion:

The approximate the depth is at 1640 meters at which the water temperature is 3°C.