Chapter 2.6, Problem 35E

a.

To determine

  $\text{An expression for the distance the whales travel in }x\text{ days}\text{.}$

Answer to Problem 35E

  $\text{The distance the whales travel in }x\text{ days is 100}x\text{ miles}\text{.}$

Explanation of Solution

Given:

The distance from the Baja Peninsula of Mexico to Alaska = $5000\text{ miles}\text{.}$

The speed of the whales = $100\text{ miles per day}\text{.}$

Concept Used:

Consider the formula of speed-distance-time:

  $\text{distance = speed}\times \text{time}$

Calculation:

As per the question,

The speed of the whales = $100\text{ miles per day}\text{.}$

Consider, $x\text{ as the number of days travelled by the whales}\text{.}$

Then, the total distance travelled by the whales in $x$ days is given by,

  $\text{distance = speed}\times \text{time}$

  $\text{distance = 100 miles per day}\times x\text{ days}$

That is,

  $\text{distance = 100}x$ .

Hence,

  $\text{The distance the whales travel in }x\text{ days is 100}x\text{ miles}\text{.}$

Conclusion:

  $\text{The distance the whales travel in }x\text{ days is 100}x\text{ miles}\text{.}$

b.

To determine

Complete the given table

Answer to Problem 35E

Explanation of Solution

Given:

Consider the equation,

  $\text{distance = 100}x$ .

Consider the table provided in the question,

Calculation:

As per the given problem

Consider the equation,

  $\text{distance = 100}x$

Where $x$ is the number of days travelled.

1. Substitute the value $x=0$ in the equation,

  $\text{distance = 100}\cdot \text{0 = 0}\text{.}$

Hence,

The distance travelled in $0$ days is $0$ miles.

2. Substitute the value $x=5$ in the equation,

  $\text{distance = 100}\cdot 5\text{ = 500}\text{.}$

Hence,

The distance travelled in $5$ days is $\text{500}$ miles.

3. Now, substitute the value $x=10$ in the equation,

  $\text{distance = 100}\cdot 10\text{ = 1000}\text{.}$

Hence,

The distance travelled in $10$ days is $\text{1000}$ miles.

4. Now, substitute the value $x=15$ in the equation,

  $\text{distance = 100}\cdot 15\text{ = 1500}\text{.}$

Hence,

The distance travelled in $15$ days is $\text{1500}$ miles.

5. Now, substitute the value $x=20$ in the equation,

  $\text{distance = 100}\cdot 20\text{ = 2000}\text{.}$

Hence,

The distance travelled in $20$ days is $\text{2000}$ miles.

6. Now, substitute the value $x=25$ in the equation,

  $\text{distance = 100}\cdot 25\text{ = 2500}\text{.}$

Hence,

The distance travelled in $25$ days is $\text{2500}$ miles.

Writing in tabulated form,

Conclusion:

The completed table is as follows:

c.

To determine

Create a scatter plot of the data in the table

Answer to Problem 35E

The scatter plot represents a straight line,

Explanation of Solution

Given information:

The table is as follows:

The time is to be plotted along x-axis and distance to be plotted along y-axis.

Graph :

Interpretation :

The scattered plot of the data represents a straight-line graph , that is with days the distance travelled also increases.

d.

To determine

Create a scatter plot of the data in the table

Answer to Problem 35E

The scatter plot represents a straight line,

Explanation of Solution

Given information:

The table is as follows:

The time is to be plotted along x-axis and distance to be plotted along y-axis.

Graph :

As per the question, to extend the plot,

Consider $y=5000$ which is the distance in miles.

So, substitute distance = $5000$ in the equation:

  $\text{distance = 100}x$

  $5000=100x$

Dividing both sides by 100,

  $\frac{5000}{100}=\frac{100}{100}x$

Therefore,

  $50=x$ , or

  $x=50$ .

Taking values of $x$ in differences of 5 as $x=30,x=35,x=40,x=45,x=50$ ,

For $x=30$ ,

  $\text{distance = y=100}\cdot 30\text{ = 3000}\text{.}$

For $x=35$ ,

  $\text{distance = y=100}\cdot 35\text{ = 3500}\text{.}$

  $\begin{array}{l}\text{for }x=40\\ \text{distance = y=100}\cdot 40\text{ = 4000}\text{.}\end{array}$

  $\begin{array}{l}\text{for }x=45\\ \text{distance = y=100}\cdot 45\text{ = 4500}\text{.}\end{array}$

  $\begin{array}{l}\text{for }x=50\\ \text{distance = y=100}\cdot 50\text{ = 5000}\text{.}\end{array}$

Tabulating the data,

Plotting the graph,

Interpretation :

The whales take 50 days to migrate from the Baja Peninsula of Mexico to Alaska.

e.

To determine

To solve the equation $\text{100}x=5000$

Answer to Problem 35E

  $\text{The value of }x\text{ is }50.$

Explanation of Solution

Given:

Consider the equation provided in the question:

  $\text{100}x=5000$

Concept Used:

Multiplicative property of equality.

Calculation:

As per the question,

  $\text{100}x=5000$

Dividing both sides by $\text{100}$ ,

  $\frac{100x}{100}=\frac{5000}{100}$

Therefore,

  $x=50$ , that is same as the value from the graph in part d.

Conclusion:

  $\text{The value of }x\text{ is }50.$