Question

A long distance phone service charges $0.30 for the first 10 minutes and $0.05 for each additional minute or fraction thereof. Use the greatest integer function to write the cost C of a call in terms of time t (in minutes). Sketch the graph of this function and discuss its continuity.

Answer 1

Answer: Our Cost function is discontinuous at every integer after x>10.

Explanation:

Since we have given that

For the first 10 minutes , the service charges = $0.30

Let the number of additional minute be 't'.

Amount charge for each additional minute = $0.05

Using the greatest integer function:

So, Cost C of a call in terms of time 't' minutes would be

`C=0.03+0.05\left \lceil t-10 \right \rceil`

As we know that Greatest integer is discontinuous at every integer.

So, our Cost function is discontinuous at every integer after x>10.