Chapter 4.2, Problem 1MP

a.

To determine

To find: the relationship between the number of months and the number of subscribers.

Explanation of Solution

Given information:

Jayden’s blog details are as follows:

Numnre of months	Number of subscribers
0	48
1	56
2	64
3	72
4	80

Calculation:

From the table it is observed that number of subscribers increases as the months passes by.

The number of subscribers increases by multiple of $8$ with the addition of $48$ in each month.

b.

To determine

To find: which column represents the dependent and independent variable.

Answer to Problem 1MP

Number of subscribers represents the dependent variables.

Number of months represents the independent variables.

Explanation of Solution

Dependent variable: dependent variable is a variable whose value depends on the value of another variable.

Independent variable: dependent variable is a variable whose value does not depends on the value of another variable.

In the table, the number of subscribers depends on the number of months.

Therefore the number of subscribers column represents the dependent variables and number of months column represents the independent variables.

c.

To determine

whether the relation is a function.

Answer to Problem 1MP

Relation is a function.

Explanation of Solution

Given information:

The given table is,

Numnre of months	Number of subscribers
0	48
1	56
2	64
3	72
4	80

The independent variables are also known as inputs and the dependent variables are also known as the outputs.

From the table, for each value of input, there is exactly one value of output therefore the given relationship between number of months and the number of subscribers.

d.

To determine

To find: the equation to represent the relationship.

Answer to Problem 1MP

The equation is,

  $y=8x+48$

Explanation of Solution

Given information:

Jayden’s blog details are as follows:

Numnre of months	Number of subscribers
0	48
1	56
2	64
3	72
4	80

Let $x$ represents the number of months and $y$ represents the number of subscribers.

Calculation:

From the table it is observed that number of subscribers increases as the months passes by.

The number of subscribers increases by multiple of $8$ with the addition of $48$ in each month.

The pattern in the relationship is written in the form of an equation as follows:

  $y=8x+48$

e.

To determine

To find: expand the table to $8$ months and the number of subscribers for $\text{8th}$ months.

Answer to Problem 1MP

Number of subscribers for $\text{8th}$ months is $112$ .

Explanation of Solution

Let $x$ represents the number of months and $y$ represents the number of subscribers.

The relationship between numbers of months and the number of subscribers is represented by the equation,

  $y=8x+48$

Therefore, the table can be expand to $\text{8}$

months as follows:

Numnre of months (x)	Number of subscribers (y)
0	48
1	56
2	64
3	72
4	80
5	88
6	96
7	104
8	112

The number of subscribers for $\text{8th}$ months is $112$ .

f.

To determine

To find: the method to find the number of subscribers after a year. .

Explanation of Solution

The relationship between numbers of months and the number of subscribers is represented by the equation,

  $y=8x+48$

The above equation can be used up to $12$ months but relationship is established between number of months and the number of subscribers. Therefore the function rule can be used to calculate the number of subscribers after a year $\left(\text{12}\text{months}\right)$ .