Question

A telephone carrier charges customer 0.99 cents for the first 10 minutes and then 0.06 for each minute beyond 10 min. If Mary uses this carrier, how long can she talk for $6.00

Answer 1

We have the following function for this problem:

`\begin{cases}f(t)=0.99,t\leq10 \\ f(t)=0.06(t-10)+0.99,t>10\end{cases}`

Where 't' represents the time in minutes, and our 'f(t)' returns the cost.

For f(t) = 6, we want to know the value for 't'. Clearly, it is not in the first interval, so let's check for t >10.

`6=0.06(t-10)+0.99`

Solving for 't':

`\begin{gathered} 5.01=0.06(t-10)_{} \\ 83.5=t-10 \\ 93.5=t \end{gathered}`

Mary can talk for 93 minutes.