Instructions: Identify the input and output of the function in the given scenario. Then, state the appropriate scales.

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 = 40m + 60[/tex] represents the total cost per month. How much money will this deal cost you after 9 months?

1. The input values for this function are [tex]\square[/tex]
2. The output values for this function are [tex]\square[/tex]
3. An appropriate scale for the [tex]x[/tex]-axis would be: [tex]\square[/tex]
4. An appropriate scale for the [tex]y[/tex]-axis would be: [tex]\square[/tex]



Answer :

Let's solve the problem step by step.

1. Identify the Input and Output Values:

The function provided is [tex]\( y = 40m + 60 \)[/tex].

- The input value [tex]\( m \)[/tex] represents the number of months.

- The output value [tex]\( y \)[/tex] represents the total cost.

Therefore:
- The input values for this function are months.
- The output values for this function are total cost.

2. Calculate the Total Cost for 9 Months:

According to the given function [tex]\( y = 40m + 60 \)[/tex], let's substitute [tex]\( m = 9 \)[/tex]:

- Total cost [tex]\( y = 40 \times 9 + 60 \)[/tex]
- Total cost [tex]\( y = 360 + 60 \)[/tex]
- Total cost [tex]\( y = 420 \)[/tex]

After 9 months, the total cost will be \[tex]$ 420. 3. Determine the Appropriate Scales for the Axes: - Since we're considering a number of months (ranging from 0 up to at least 9), a reasonable scale for the \( x \)-axis (months) would be from 0 to 12 months to cover enough range. - Given that each month costs \$[/tex] 40 and the initial cost of the cell phone is \$ 60, we need a scale that accommodates the total cost. For up to 12 months, the formula [tex]\( y = 40m + 60 \)[/tex] gives a maximum value of [tex]\( y = 40 \times 12 + 60 = 480 \)[/tex]. Therefore, an appropriate scale for the [tex]\( y \)[/tex]-axis (total cost) would be from 0 to 500 dollars.

4. Summary of Answer:

- The input values for this function are months.
- The output values for this function are total cost.
- An appropriate scale for the [tex]\( x \)[/tex]-axis would be: 0 to 12 months.
- An appropriate scale for the [tex]\( y \)[/tex]-axis would be: 0 to 500 dollars.