Chapter 4.3, Problem 1P

(a)

To determine

TO graph: The function represented by the table is to be sketch on the graph and whether the function is linear or nonlinear is to be checked.

Answer to Problem 1P

The graph is,

  

The function is non-linear.

Explanation of Solution

The given table is,

n(number of cuts)	A(fraction of original area remaining)
1	1/2
2	1/4
3	1/8
4	1/16

The graph between the number of cuts and the fraction of area remaining is plotted as follows:

  

Non-linear function: the linearity and non-linearity of a function is checked by its graph. If the graph is represented by a line, function is said to be linear while the graph of non-linear function is not represented by a line.

The above graph does not represent a line therefore the function is non-linear.

(b)

To determine

The value of area in part (a) is to be checked.

Answer to Problem 1P

The value of area may be zero.

Explanation of Solution

From the graph in part (a), the fraction of remaining is decreeing as the number of cuts increases. After a large number of cuts, the value of area may be zero.