Chapter 8.7, Problem 30E

a.

To determine

To graph:

Our given function using a graphing calculator by replacing d with x and $s(d)$ with y .

Answer to Problem 30E

The graph of our given function would look like:

  

Explanation of Solution

Given:

Surveyors measured the speed of the current below a dam on the Columbia river in Washington. Based on their data, the speed (in feet per second) can be approximated by $s(d)=-0.117d+1.68,$ where d is depth (in feet) below the river’s surface.

Calculation:

Upon replacing d with x and $s(d)$ with y , we will get:

  $y=-0.117x+1.68,$

To graph our function, we will use Desmos and get our required graph as shown below:

  

b.

To determine

To describe:

What happens to the speed of the current as you go deeper below the river’s surface?

Answer to Problem 30E

The speed of the current decreases as you go deeper below the river’s surface.

Explanation of Solution

Given:

Surveyors measured the speed of the current below a dam on the Columbia river in Washington. Based on their data, the speed (in feet per second) can be approximated by $s(d)=-0.117d+1.68,$ where d is depth (in feet) below the river’s surface.

Calculation:

Upon looking at our graph in part (a), we can see that as x increases, the value of y decreases.

Therefore, the speed of the current decreases as you go deeper below the river’s surface.

c.

To determine

To approximate:

The speed of the current at a depth of 9 feet.

Answer to Problem 30E

The speed of the current at a depth of 9 feet would be approximately 0.63 feet per second.

Explanation of Solution

Given:

Surveyors measured the speed of the current below a dam on the Columbia river in Washington. Based on their data, the speed (in feet per second) can be approximated by $s(d)=-0.117d+1.68,$ where d is depth (in feet) below the river’s surface.

Calculation:

To find speed of the current at a depth of 9 feet, we will substitute $d=9$ in our given function as:

  $\begin{array}{l}s(d)=-0.117d+1.68\\ s(9)=-0.117(9)+1.68\\ s(9)=-1.053+1.68\\ s(9)=0.627\\ s(9)\approx 0.63\end{array}$

Therefore, the speed of the current at a depth of 9 feet would be approximately 0.63 feet per second.