felder1trevion
Answered

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Instructions: Answer the following questions about the situation.

A cell phone company is offering its customers the following deal: You can buy a new cell phone for [tex] \[tex]$60 [/tex] and pay a monthly flat rate of [tex] \$[/tex]40 [/tex] per month for unlimited calls. The function [tex] y = 40x + 60 [/tex] represents the total cost per month.

1. How much money will this deal cost you after 9 months?

2. How much would it cost for 0 months?

3. This represents the [tex]$\square$[/tex] of the function.

Sagot :

GinnyAnswer
Sure, let's solve these questions step by step.

### Part 1: Calculating the Total Cost After 9 Months

The function for the total cost [tex]\( y \)[/tex] in dollars per month is given by:

[tex]\[ y = 40x + 60 \][/tex]

Where:
- [tex]\( x \)[/tex] represents the number of months you use the service.

We are asked to calculate the cost after 9 months. So, we'll substitute [tex]\( x = 9 \)[/tex] into the function:

[tex]\[ y = 40(9) + 60 \][/tex]

First, we multiply 40 by 9:

[tex]\[ 40 \times 9 = 360 \][/tex]

Next, we add 60 to 360:

[tex]\[ 360 + 60 = 420 \][/tex]

So, the total cost after 9 months is [tex]\( \$420 \)[/tex].

### Part 2: Calculating the Total Cost for 0 Months

Now, we need to find out the cost for 0 months. Substitute [tex]\( x = 0 \)[/tex] into the function:

[tex]\[ y = 40(0) + 60 \][/tex]

First, we multiply 40 by 0:

[tex]\[ 40 \times 0 = 0 \][/tex]

Next, we add 60 to 0:

[tex]\[ 0 + 60 = 60 \][/tex]

So, the total cost for 0 months is [tex]\( \$60 \)[/tex].

### Part 3: Interpreting [tex]\( y \)[/tex] for 0 Months

The cost for 0 months, which is [tex]\( \$60 \)[/tex], represents the initial purchase cost of the cell phone. This is also recognized as the y-intercept of the function [tex]\( y = 40x + 60 \)[/tex].

Therefore, the total cost after 9 months is [tex]\( \$420 \)[/tex] and the cost for 0 months is [tex]\( \$60 \)[/tex]. The cost for 0 months represents the initial purchase cost of the cell phone.
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