Question

The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after 32minutes of calls is $24.88, and the remaining credit after 48 minutes of calls is $22.32. What is the remaining credit after 56 minutes of calls?

Answer 1

We are given:

`\begin{gathered} f(32)=24.88 \\ \Rightarrow(x_1,y_1)=(32,24.88) \\ (x_1,y_1)=(32,24.88) \\ \\ f\mleft(48\mright)=22.32 \\ \Rightarrow(x_2,y_2)=(48,22.32) \\ (x_2,y_2)=(48,22.32) \end{gathered}`

We will calculate the slope as shown below:

`\begin{gathered} slope(m)=(y_2-y_1)/(x_2-x_1) \\ slope(m)=(22.32-24.88)/(48-32) \\ slope(m)=-(2.56)/(16) \\ slope(m)=-0.16 \end{gathered}`

The formula for a linear function is given as:

`\begin{gathered} y=mx+b \\ (x,y)=(x_1,y_1)=(32,24.88) \\ \Rightarrow24.88=-0.16(32)+b \\ 24.88=-5.12+b \\ \text{Add ''5.12'' to both sides, we have:} \\ 24.88+5.12=b \\ 30=b\Rightarrow b=30 \\ b=30 \end{gathered}`

The equation thus becomes:

`\begin{gathered} y=-0.16x+30 \\ when\colon x=56 \\ y=-0.16(56)+30 \\ y=-8.96+30 \\ y=21.04 \\ \\ \therefore The\text{ remaining credit after 56 minutes of call is \$21.04} \end{gathered}`

Therefore, the remaining credit after 56 minutes of call is $21.04