Question

question 6: cellular data plan
a cell phone company charges for data usage as follows:

• $25 for up to 2 gb of data.
• $10 per gb for usage between 2 and 6 gb.
• $5 per gb for usage beyond 6 gb.

this is modeled by:

$$ d(x)=\\left\\{\
LATEXBLOCK0
\ ight.\
LATEXBLOCK1
$$

find the cost for using 1 gb, 5 gb, and 8 gb of data. explain what the results mean in terms of the data plan.

Explanation:

Step1: Calculate cost for 1 GB

Since \(0 < 1<2\), use \(D(x)=25\).

Step2: Calculate cost for 5 GB

Since \(2 < 5<6\), use \(D(x)=25 + 10(x - 2)\).
Substitute \(x = 5\) into \(D(x)=25+10(x - 2)\):
\(D(5)=25+10\times(5 - 2)=25 + 30=55\).

Step3: Calculate cost for 8 GB

Since \(8>6\), use \(D(x)=65+5(x - 6)\).
Substitute \(x = 8\) into \(D(x)=65+5(x - 6)\):
\(D(8)=65+5\times(8 - 6)=65 + 10=75\).

Answer:

The cost for using 1 GB is \(\$25\), for 5 GB is \(\$55\), and for 8 GB is \(\$75\).