# Cost function

• Aug 19th 2012, 11:37 AM
Jerry99
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 ?

• Aug 19th 2012, 01:17 PM
Plato
Re: Cost function
Quote:

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: $\displaystyle C(t) = 9.90 + 0.90\left\lceil {t - 1} \right\rceil$
• Aug 19th 2012, 01:23 PM
Soroban
Re: Cost function
Hello, Jerry99!

That cost function is scary . . .

Quote:

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 $\displaystyle t$ 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 $\displaystyle t-1$ minutes.
The "or fraction thereof" means that they will round up when a fraction is involved.
. . Hence, the remaining time is $\displaystyle \lceil t-1\rceil$ minutes (ceiling function).

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

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
• Aug 19th 2012, 01:47 PM
Jerry99
Re: Cost function
Ok thanks guys