Question

NEED HELP ASAP! WILL GIVE MEDAL!

Answer 1

A. Write a piecewise-defined function (with a minimum of two pieces) for each company. The piecewise function needs to accurately represent the following features: base plan and then an overage charge for exceeding this allotment of minutes.

Answer 2

x = a, t ≤ T
x = aT + bt, t≥T

Answer 3

I need to get that information from these companies: Company A:at&t
Company B: Sprint

Answer 4

Let's say a company \(X\) has a plan:
You get \(\phi\) free minutes per month for \(\kappa\) dollars and \(\theta\) dollars per minute if you exceed the \(\phi\) minutes per month. So then a Piecewise function \(\chi(\mu)\) which returns the cost per month in \(\chi\) dollars for any \(\mu\) amount of minutes is the following:
\[\chi(\mu)=\left\{\eqalign{
&\kappa;\phantom{.............}0\lt\mu\lt\phi \\
&\theta(\mu-\phi)+\kappa ;\phantom{..}0 \\
}\right.\]
...I think...

Answer 5

Err sorry... wait

Answer 6

Yep the answer would be that:
\[\chi(\mu)=\left\{\eqalign{
&\kappa;\phantom{.............}0\le\mu\leq\phi \\
&\theta(\mu-\phi)+\kappa ;\phantom{..}\mu\gt\phi \\
}\right.\]

Answer 7

How would this information fit into that equation? Only going up to 6GB.

Answer 8

Okay so what you have here are companies which charge \(\chi\) dollars for \(\mu\) gigabytes right?

Which company you want?

Answer 9

At&t and Sprint.

Answer 10

Okay so let's say for AT&T. We know that up to 4Gb, it will always cost us $30 Right?

Answer 11

Yes.

Answer 12

So then we also know that from 4Gb to 6Gb (which is a difference of 2Gb), they charge an extra of $10 so if it is $10/2Gb, then we know that the price rate is $5/Gb
So then you can get the following variables:
\[\eqalign{
&\kappa=30 \\
&\theta=5 \\
&\phi=4 \\

}\]
So therefore we can get the following equation:
\[\chi(\mu)=\left\{\eqalign{
&$30;\phantom{.............}0\le\mu\leq4 \\
&$5(\mu-4)+30 ;\phantom{..}\mu\gt4 \\
}\right.

\]

Answer 13

Cool?

Answer 14

Okay, that makes sense.

Answer 15

Cool would you like the other one too or youre fine? :)

Answer 16

If you have time that would be great. :)

Answer 17

Alright. It's kinda similar just changing around \(\kappa\), \(\theta\), and \(\phi\)
So then we have the fact that up until 3Gb, the price is 34.99;

We also know that in an extra 15Gb, the price is increased $15 so therefore;

\[\chi(\mu)=\left\{\eqalign{
&$34.99;\phantom{.............}0\le\mu\leq3 \\
&$5(\mu-3)+34.99 ;\phantom{..}\mu\gt3 \\
}\right.\]

Answer 18

I am confused on the values for the following ?
\[\chi = ?
\mu = ? \]

Answer 19

Oh it doesn't matter it's a function so it will have an independent variable \(\mu\) and a dependent one \(\chi\)

Answer 20

Okay. There is a second part to this. Can you help me with it too please?

Answer 21

Use technology to graph each piecewise-defined function on a separate piece of paper; label axis appropriately and clearly identify the intervals. Some possible choices:

www.desmos.com

http://www.fooplot.com