Respuesta :
Answer:
The monthly cost for 85 minutes of call is;
[tex]\text{\$22.83}[/tex]Explanation:
Given that the monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes).
[tex]C(x)=mx+b[/tex]The monthly cost for 43 minutes of calls is $18.21 ;
[tex]18.21=43m+b\text{ -------1}[/tex]the monthly cost for 102 minutes is $24.70;
[tex]24.70=102m+b\text{ -----------2}[/tex]to get m and b, subtract equation 1 from 2;
[tex]\begin{gathered} 24.70=102m+b \\ - \\ 18.21=43m+b \\ = \\ 6.49=59m \\ m=\frac{6.49}{59} \\ m=0.11 \end{gathered}[/tex]to get b, substitute the value of m into equation1;
[tex]\begin{gathered} 18.21=43m+b \\ b=18.21-43(0.11) \\ b=18.21-4.73 \\ b=13.48 \end{gathered}[/tex]So, the linear function that can represent the monthly cost of phone plan is;
[tex]C(x)=0.11x+13.48[/tex]For the monthly cost for 85 minutes of call, we have;
[tex]\begin{gathered} C(85)=0.11(85)+13.48 \\ C(85)=\text{ \$22.83} \end{gathered}[/tex]Therefore, the monthly cost for 85 minutes of call is;
[tex]\text{\$22.83}[/tex]