Part A.
Let x be the number of months. Since the rate is $44 per month and the initial fee is $48, the linear model is:
[tex]C(x)=44x+48[/tex]
where C(x) denotes the total cost.
Part B.
In this case, we must substitute x=6 into our linear model. It yields,
[tex]C(6)=44(6)+48[/tex]
which gives
[tex]\begin{gathered} C(6)=264+48 \\ C(6)=312 \end{gathered}[/tex]
Therefore, after 6 months, the total cost will be $312.
Part C.
In this case, the second company has a rate of $62 per month with no initial fee. Then, the linear model for the second company is
[tex]\begin{gathered} B(x)=62x+0 \\ or\text{ equivalently, } \\ B(x)=62x \end{gathered}[/tex]
where now B(x) denotes the total cost for the second company.
Then, since you have $620, we can compare both companies by substituting the total cost of $620 into the two linear models, that is,
[tex]\begin{gathered} 620=44x+48 \\ \text{and} \\ 620=62x \end{gathered}[/tex]
and finc x for each model.
Then, the first model yields,
[tex]\begin{gathered} 44x=620-48 \\ 44x=572 \\ x=\frac{572}{44} \\ x=13\text{ months} \end{gathered}[/tex]
and the second equation gives
[tex]\begin{gathered} x=\frac{620}{62} \\ x=10\text{ months} \end{gathered}[/tex]
By comparing both result, we can see that the best choice in the first company with 13 months
