# Math Help - Cost function

1. ## Cost function

I'm having issues remembering how to create cost functions:

For a long-distance phone call, a hotel charges $9.89 for the first minute and$0.90 for each additional minute or fraction thereof. A formula for the cost is given below, where t is the time in minutes

So the function is ?

C(t)=9.89-0.90[[-(t-1)]]

Do I just distribute that out?

Use a graphing utility to graph the cost function for 0 < t ≤ 5.

How do I set the paramaters for this requirement to graph this on my calculator ?

2. ## Re: Cost function

Originally Posted by Jerry99
I'm having issues remembering how to create cost functions:
For a long-distance phone call, a hotel charges $9.89 for the first minute and$0.90 for each additional minute or fraction thereof. A formula for the cost is given below, where [I]t is the time in minutes
So the function is ?
C(t)=9.89-0.90[[-(t-1)]]
I would use the ceiling function: $C(t) = 9.90 + 0.90\left\lceil {t - 1} \right\rceil$

3. ## Re: Cost function

Hello, Jerry99!

That cost function is scary . . .

For a long-distance phone call, a hotel charges $9.89 for the first minute and$0.90 for each additional minute or fraction thereof.
A formula for the cost is given below, where $t$ is the time in minutes

So the function is ?

C(t) = 9.89 - 0.90[[-(t-1)]] . Weird!

Use a graphing utility to graph the cost function for 0 < t ≤ 5.

How do I set the paramaters for this requirement to graph this on my calculator?

The hotel charges $9.89 for the first minute. It charges$0.90 per minute for the other $t-1$ minutes.
The "or fraction thereof" means that they will round up when a fraction is involved.
. . Hence, the remaining time is $\lceil t-1\rceil$ minutes (ceiling function).

The cost is: . $C \:=\:9.89 + 0.90\lceil t-1\rceil$

The graph looks like this.

Code:
          |
$13.49 + o=====♠ | : : | : :$12.59 +                 o=====♠     :
|                 :     :     :
|                 :     :     :
$11.69 + o=====♠ : : | : : : : | : : : :$10.79 +     o=====♠     :     :     :
|     :     :     :     :     :
|     :     :     :     :     :
\$9.89 o=====♠     :     :     :     :
|     :     :     :     :     :
|     :     :     :     :     :
|     :     :     :     :     :
- - * - - + - - + - - + - - + - - + - -
0     1     2     3     4     5  minutes

4. ## Re: Cost function

Ok thanks guys