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 limit

When the amount of data used \(d\) satisfies \(0\leq d\leq5\) (within the 5 - GB limit), the monthly cost is a fixed \(79.95\) dollars. So, \(C(d)=79.95\) for \(0\leq d\leq5\).

Step2: Analyze data - usage over limit

When \(d > 5\), the base - cost of \(79.95\) dollars is still there, and there is an additional charge of \(10\) dollars per additional gigabyte. The number of additional gigabytes is \(d - 5\). So the cost function is \(C(d)=79.95+10(d - 5)\) for \(d>5\).

Answer:

A. \(C(d)=

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

\)