Chapter 9.1, Problem 35STP

To determine

To identify: which tables contains values that satisfy function $\mathrm{c}\left(\mathrm{d}\right)=3.50\mathrm{d}$

Answer to Problem 35STP

Table A satisfies the function.

Explanation of Solution

Given information:

  

  

  

  

Calculation:

As all the optional values of d are from 1 to 4

Check the function value at these points

  $\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{d}=1$

  $\begin{array}{l}\mathrm{c}\left(\mathrm{d}\right)=3.50\mathrm{d}\\ \mathrm{c}\left(\mathrm{d}\right)=3.50\left(1\right)\\ \mathrm{c}\left(\mathrm{d}\right)=3.50\end{array}$

  $\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{d}=2$

  $\begin{array}{l}\mathrm{c}\left(\mathrm{d}\right)=3.50\mathrm{d}\\ \mathrm{c}\left(\mathrm{d}\right)=3.50\left(2\right)\\ \mathrm{c}\left(\mathrm{d}\right)=7.00\end{array}$

  $\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{d}=3$

  $\begin{array}{l}\mathrm{c}\left(\mathrm{d}\right)=3.50\mathrm{d}\\ \mathrm{c}\left(\mathrm{d}\right)=3.50\left(3\right)\\ \mathrm{c}\left(\mathrm{d}\right)=10.50\end{array}$

  $\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{d}=4$

  $\begin{array}{l}\mathrm{c}\left(\mathrm{d}\right)=3.50\mathrm{d}\\ \mathrm{c}\left(\mathrm{d}\right)=3.50\left(4\right)\\ \mathrm{c}\left(\mathrm{d}\right)=14.00\end{array}$

Hence,

  $\begin{array}{l}\mathrm{d}=1\Rightarrow \mathrm{c}\left(\mathrm{d}\right)=3.50\\ \mathrm{d}=2\Rightarrow \mathrm{c}\left(\mathrm{d}\right)=7.00\\ \mathrm{d}=3\Rightarrow \mathrm{c}\left(\mathrm{d}\right)=10.50\\ \mathrm{d}=4\Rightarrow \mathrm{c}\left(\mathrm{d}\right)=14.00\end{array}$

Therefore, the table A satisfies the function.