Question

jordans cell phone plan includes 5 gigabytes (gb) of data per month and has a monthly cost of $79.95. if jordan uses more than 5 gb of data within the month, there is a charge of $10 per additional gigabyte of data used. function c is used to model jordans monthly cell phone bill, where d is the number of gigabytes of data used and c(d) is the cost in dollars. which of the following defines function c? a c(d) = {79.95 for 0 ≤ d ≤ 5; 79.95 + 10(d - 5) for d > 5} b c(d) = {79.95 for 0 ≤ d ≤ 5; 79.95 + 10d for d > 5} c c(d) = {79.95 for 0 ≤ d ≤ 5; 79.95d + 10 for d > 5} d c(d) = 79.95 + 10d

Explanation:

Step1: Analyze data - usage within 5GB

When $0\leq d\leq5$, the monthly cost is a fixed $79.95$, so $C(d)=79.95$ in this range.

Step2: Analyze data - usage over 5GB

When $d > 5$, the base - cost is $79.95$. The number of additional gigabytes is $d - 5$, and the cost per additional gigabyte is $10$. So the cost is $79.95+10(d - 5)$.

Answer:

A. $C(d)=

$$\begin{cases}79.95&\text{for }0\leq d\leq5\\79.95 + 10(d - 5)&\text{for }d>5\end{cases}$$

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