Chapter 6.6, Problem 49CCR

a.

To determine

To find: An equation to show number of minutes spent jogging $m$ for each day $d$ .

Answer to Problem 49CCR

The required equation is $m=8d-1$ .

Explanation of Solution

Given information:

The table that shows the amount of time Craig spends jogging every day.

He increases the time he jogs every day.

  $m$ represents number of minutes spent jogging.

  $d$ represents Taking first two days data from given table

We get

  $\begin{array}{l}\left(d_1,m_1\right)=\left(1,7\right)\\ \left(d_2,m_2\right)=\left(2,15\right)\end{array}$

We know

Two points slope formula

Using that

We get

  $\begin{array}{l}m-m_1=\frac{m_2-m_1}{d_2-d_1}\left(d-d_1\right)\\ \Rightarrow m-7=\frac{15-7}{2-1}\left(d-1\right)\\ \Rightarrow m-7=\frac{8}{1}\left(d-1\right)\\ \Rightarrow m-7=8\left(d-1\right)\\ \Rightarrow m-7=8d-8\\ \Rightarrow m=8d-8+7\\ \Rightarrow m=8d-1\end{array}$

This equation is satisfied by all the given points of the table.

Therefore

The required equation is $m=8d-1$ .

a.

To determine

To find:How many minutes will Craig jog during day 9.

Answer to Problem 49CCR

Craig will jog 71 minutes during day 9.

Explanation of Solution

Given information:

The table that shows the amount of time Craig spends jogging every day.

He increases the time he jogs every day.

  $d=9$

  $m$ represents number of minutes spent jogging.

  $d$ represents The equation that represents the given situation is $m=8d-1$ .

Substitute $d=9$

We get

  $\begin{array}{l}m=8d-1\\ \Rightarrow m=8\left(9\right)-1\\ \Rightarrow m=72-1\\ \Rightarrow m=71\end{array}$

Therefore,

Craig will jog 71 minutes during day 9.