The problem describes two cell phone plans: Company C charges \$10 per month plus \$15 per gigabyte, and Company D charges a flat \$80 per month for unlimited data. The problems asks a few questions about these plans, including comparisons of costs and finding the data usage where the cost of Company C's plan reaches a certain value. We must also graph the two cost functions.

1. Problem Description

The problem describes two cell phone plans: Company C charges \10 per month plus \15 per gigabyte, and Company D charges a flat \$80 per month for unlimited data. The problems asks a few questions about these plans, including comparisons of costs and finding the data usage where the cost of Company C's plan reaches a certain value. We must also graph the two cost functions.

2. Solution Steps

a. The statement $C(2) = 40$ means that if you use 2 gigabytes of data with Company C's plan, the monthly cost will be \$

4

0. b. We need to determine which is less, $C(4)$ or $D(4)$.

First, we calculate $C(4)$. The cost of Company C is given by the formula

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

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

The cost of Company D is constant at \$80, so$D(g) = 80$for all$g$. Therefore,$D(4) = 80$.

Since $70 < 80$, $C(4) < D(4)$. This means using 4 gigabytes costs less with Company C's plan than with Company D's plan.

c. We need to determine which is less, $C(5)$ or $D(5)$.

We calculate $C(5)$:

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

Since $D(5) = 80$, we have $D(5) < C(5)$. This means using 5 gigabytes costs less with Company D's plan than with Company C's plan.

d. We want to find the value of $g$ for which $C(g) = 130$. We set $C(g)$ equal to 130 and solve for $g$.

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

$15g = 130 - 10 = 120$

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

So, $C(8) = 130$.

e. We need to draw the graphs of the two functions. The cost of Company C is $C(g) = 10 + 15g$, which is a linear function with a y-intercept of 10 and a slope of

1

5. The cost of Company D is $D(g) = 80$, which is a horizontal line at $y = 80$.

3. Final Answer

a. If you use 2 gigabytes of data with Company C's plan, the monthly cost will be \$

4

0. b. $C(4) < D(4)$. This means using 4 gigabytes costs less with Company C's plan.

c. $D(5) < C(5)$. Using 5 gigabytes costs less with Company D's plan. $C(5) = 85$ and $D(5) = 80$.

d. $g = 8$

e. The graph of $C(g) = 10 + 15g$ is a line with a y-intercept of 10 and a slope of

1

5. The graph of $D(g) = 80$ is a horizontal line at $y = 80$.