The problem describes two cell phone plans. Company C charges $10 per month plus $15 per gigabyte, while Company D charges $80 per month with unlimited data. We are asked to answer a few questions relating to the costs of the plans.

1. Problem Description

The problem describes two cell phone plans. Company C charges $10 per month plus$15 per gigabyte, while Company D charges $80 per month with unlimited data. We are asked to answer a few questions relating to the costs of the plans.

2. Solution Steps

a. $C(2) = 40$ means that the cost of Company C's plan is $40 when 2 gigabytes of data are used.

b. First, we need to determine the equations for C(g) and D(g).

$C(g) = 10 + 15g$

$D(g) = 80$

Then we calculate $C(4)$ and $D(4)$:

$C(4) = 10 + 15(4) = 10 + 60 = 70$

$D(4) = 80$

Since $70 < 80$, $C(4) < D(4)$.

This means that if you use 4 gigabytes of data, Company C's plan is cheaper than Company D's plan.

c. Now, we compare $C(5)$ and $D(5)$:

$C(5) = 10 + 15(5) = 10 + 75 = 85$

$D(5) = 80$

Since $85 > 80$, $C(5) > D(5)$.

This means that if you use 5 gigabytes of data, Company D's plan is cheaper than Company C's plan.

d. We want to find $g$ such that $C(g) = 130$.

$C(g) = 10 + 15g = 130$

$15g = 130 - 10$

$15g = 120$

$g = \frac{120}{15} = 8$

So, $C(8) = 130$.

3. Final Answer

a. The cost of Company C's plan is $40 when 2 gigabytes of data are used.

b. $C(4) < D(4)$. If you use 4 gigabytes of data, Company C's plan is cheaper than Company D's plan.

c. $C(5) > D(5)$. If you use 5 gigabytes of data, Company D's plan is cheaper than Company C's plan.

d. $g=8$