Chapter 3.2, Problem 9CYU

To determine

To find:

Zero, domain, and range of the given function $w=30-\frac{3}{4}n$ and to write its mean in the context of given situation.

Answer to Problem 9CYU

Zero of the given function is $n=40$ that means after 40 papers delivered, the weight of bag starts decreasing.

Accordingly, its domain is $\{0,1,2,3,\dots ,40\}$ and its range in set building form is $\{w:w\le 30,w\text{is a multiple of}\frac{3}{4}\}$ .

Explanation of Solution

Given information:

The function $w=30-\frac{3}{4}n$ represents the weight w in pounds of the papers in T`s newspaper delivery bag after he delivers n newspapers.

Concept used:

Zero of an equation is obtained by putting it equal to 0 and then solving it for independent variable n .

Also set of all values of n is its domain and set of all values of w is its range.

Calculation:

Put in $w=0$ and on solve it for n ,

  $0=30-\frac{3}{4}n$

Or, $30=\frac{3}{4}n$

Now on cross multiplying,

  $n=\frac{30\times 4}{3}=40$

So, only zero of this equation is $n=40$ $.$

Thus, after delivering 40 newspaper the weight of the bag remains 0 pound. So, the values of n may be from 1 to 40 and accordingly the values of variable w may be from 0 to 30 .

So, n may be smaller or equal to 40. So, domain of this function will be an infinite set $\{0,1,2,3,\dots ,40\}$ and accordingly the range of the function as different weights of the bag will be $\{w:w\le 30,w\text{is a multiple of}\frac{3}{4}\}$ .

Conclusion:

Value $n=40$ means that paper bag has maximum 40 newspapers.