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.
