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You consider buying a phone from one of two cell phone carriers. The table shows the total costs (in dollars) of the phone and service for different numbers of months at Carrier A . The total cost y (in dollars) of the phone and x months of service at Carrier B is represented by the equation y=55x+300 . Which carrier has the lower initial fee? After how many months of service are the total costs the same?

Respuesta :

Using linear functions, we have that:

  • Carrier B has the lower initial fee.
  • They will have the same amount after 10 months.

What is the missing information?

The table for Carrier A is missing and has two points (3,500) and (6,650).

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

For Carrier B, the function is:

yB(x) = 55x + 300.

For Carrier A, when in 3 months, the price increases by $150, hence the slope is:

m = 150/3 = 50.

Hence:

yA = 50x + b.

When x = 3, y = 500, hence we use it to find b as follows.

500 = 50(3) + b

b = 350.

Then:

yA = 50x + 350.

Due to the lower intercept, we have that:

Carrier B has the lower initial fee.

They will have the same amount when:

yA = yB.

Hence:

50x + 350 = 55x + 300

5x = 50

x = 10 months.

More can be learned about linear functions at https://brainly.com/question/24808124

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