Chapter 9.3, Problem 23PPS

a.

To determine

To write an equation representing the mileage each day as a function of the number of days she rides her bike.

Answer to Problem 23PPS

The required function is $m=\frac{5000}{d}$ .

Explanation of Solution

Given information:

The given statement is:

“Marina’s New Year’s resolution is to ride her bike $5000\text{ miles}$ .”

The mileage Marina rides each day is $m$ and the number of days is $d$ .

The equation representing the mileage each day as a function of the number of days she rides her bike can be written as:

  $m=\frac{5000}{d}$ .

Hence, the required function is $m=\frac{5000}{d}$ .

b.

To determine

To graph the function.

Explanation of Solution

Given information:

The given function is:

  $m=\frac{5000}{d}$

Graph:

This represents a transformation of the graph of $f\left(x\right)=\frac{1}{x}$ .

  $a=5000$ : The graph is expanded.

  $h=0$ : There is an asymptote at $f=0$ .

  $k=0$ : There is an asymptote at $m=0$ .

The graph of the function is:

  

Interpretation:

The domain of the graph is all real numbers not equal to $0$ and the range is all real numbers except $0$ .

c.

To determine

To calculate how many miles should she ride each day, if she rides her bike every day of the year.

Answer to Problem 23PPS

Marina has to travel $13.7\text{ miles}$ per day.

Explanation of Solution

Given information:

The given statement is:

“Marina’s New Year’s resolution is to ride her bike $5000\text{ miles}$ .”

The function is $m=\frac{5000}{d}$ .

Calculation:

The miles travelled per day can be calculated by:

  $\begin{array}{l}m=\frac{5000}{d}\\ m=\frac{5000}{365}\\ m=13.7\text{ miles}\end{array}$

Hence, Marina has to travel $13.7\text{ miles}$ per day.