Question

Jane has a pre-paid cell phone with Splint. She can't remember the exact costs, but her plan has a monthly fee and a charge for each minute of calling time. In June she used 100 minutes and the cost was $54.00. In July she used 660 minutes and the cost was $138.00.
Express the monthly cost C as a function of x, the number of minutes of calling time she used.

Answer 1

Answer:

$a =\frac{138-54}{660-100}= 0.15$

And using the minutes from June we can find the value for b the intercept

$54 = 0.15*100 +b$

$b = 39$

And the function would be:

$C(x) = 0.15 x+ 39$

Step-by-step explanation:

For this case we define the following notation first:

C represent the cost for a given month

x represent the number of minutes of calling time she used

And we want to find a function of C in terms of x

We have the following info:

June

x =100 , C = 54

July

x =660 , C = 138

For this case we can assume that we can use a linear function since we have just two points given, and the general formula would be:

$C(x) = ax +b$

Where a is the slope and can be estimated as:

$a =\frac{138-54}{660-100}= 0.15$

And using the minutes from June we can find the value for b the intercept

$54 = 0.15*100 +b$

$b = 39$

And the function would be:

$C(x) = 0.15 x+ 39$