Question

A cell phone plan has a basic charge of $40 a month. The plan includes 600 free minutes and charges 10 cents for each additional minute of usage. Write the monthly cost C (in dollars) as a function of the number x of minutes used.

Answer 1

`C(x) = \left \{ {{40, x \leq 600} \atop {40 + 0.01(x - 600), x \geq 600}} \right`

Explanation:

The plan is

$40 a month for 600 free minutes.

For each extra minute

10 cents are charged.

So the cost function is a piecewise function, that is, it has one definition if the number of minutes is below 600 and one if above.

Below 600 minutes

No matter the number of minutes, you will pay 40. So

`C(x) = 40, x \leq 600`

Above 600 minutes

For the first 600 minutes, you pay just $40.

For each extra minutes above 600, you pay $0.1l, on top of the initial $40. So

`C(x) = 40 + 0.01(x - 600), x \geq 600`

Write the monthly cost C (in dollars) as a function of the number x of minutes used.

`C(x) = \left \{ {{40, x \leq 600} \atop {40 + 0.01(x - 600), x \geq 600}} \right`