Chapter 3.1, Problem 17E

a.

To determine

To find: the independent and dependent variable.

Answer to Problem 17E

Independent variable: x

Dependent variable: y

Explanation of Solution

Given:

The function $y=25x+500$ represents monthly rent y (in dollars) when rent is paid x days late.

Here, the independent variable is x and the dependent variable is y as the amount paid as rent depends on the how many days late is the rent paid.

b.

To determine

To find: range when the domain is 0, 1, 2, 3, 4 and 5.

Answer to Problem 17E

  $500,525,550,575,600,625$

Explanation of Solution

Given:

The function $y=25x+500$ represents monthly rent y (in dollars) when rent is paid x days late.

To find the range corresponding to the domain0, 1, 2, 3, 4 and 5, substitute these value in the given function and find the corresponding y values.

Substitute $x=0$ ,

  $\begin{array}{c}y\left(0\right)=25\left(0\right)+500\\ =0+500\\ =500\end{array}$

Substitute $x=1$ ,

  $\begin{array}{c}y\left(1\right)=25\left(1\right)+500\\ =25+500\\ =525\end{array}$

Substitute $x=2$ ,

  $\begin{array}{c}y\left(2\right)=25\left(2\right)+500\\ =50+500\\ =550\end{array}$

Substitute $x=3$ ,

  $\begin{array}{c}y\left(3\right)=25\left(3\right)+500\\ =75+500\\ =575\end{array}$

Substitute $x=4$ ,

  $\begin{array}{c}y\left(4\right)=25\left(4\right)+500\\ =100+500\\ =600\end{array}$

Substitute $x=5$ ,

  $\begin{array}{c}y\left(5\right)=25\left(5\right)+500\\ =125+500\\ =625\end{array}$

The range is $500,525,550,575,600,625$ .