Question

The cost of a cell phone is $700. According to the cellular device contract, you will need to be $0.22 per minute for first 500. Write the function that models the total cost of the cell phone bill for the first 500 min. What is the domain of the function?

Answer 1

`C = 700+0.22m`

Domain is [0,500] or
`0 \leq m\leq 500`

Explanation:

We are given that:

Cost of cell phone is $700.

Cost per minute for the first 500 calls is $0.22 per minute.

To find:

Function to model total cost of the cell phone bill for the first 500 minutes.

And domain of the function = ?

Solution:

Here, Total Cost is the sum of cost of cell phone, plus the cost of calls.

Total Cost = Cost of cell Phone + Cost of calls

We have the cost of cell phone as $700.

and cost of calls is $0.22 per minute up to 500 minutes.

Let the number of minutes for the calls is m. (m
`\leq` 500)

So, cost for m number of minutes of calls = m
`*` cost per minute

cost for m number of minutes of calls =
`0.22 * m`

Let the Total Cost be represented as C.

So, we can write the cost function as:

`C = 700+0.22m \ \{0\leq m\leq500\}`

Domain of a function is the valid input value to the function for which the output is defined.

Here, the domain is [0, 500] i.e. 0 and 500 are inclusive.

So, the answer is:

`C = 700+0.22m`

Domain is [0,500] or
`0 \leq m\leq 500`