Question

Jane has a pre-paid cell phone with NextFell. 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 430 minutes and the cost was $150.00. In July she used 880 minutes and the cost was $285.00.

Answer 1

A)

In order to find the function for the cost C, we can use the slope-intercept form of a linear equation:

`C=mx+b`

Where m is the slope and b is the y-intercept.

To calculate the value of m, we can use the formula below for the slope between two points (x1, y1) and (x2, y2):

`m=(y_2-y_1)/(x_2-x_1)`

Since x is the number of minutes and C is the cost function, we can use the ordered pairs (x, C). So, using the points (430, 150) and (880, 285), we have:

`m=(285-150)/(880-430)=(135)/(450)=0.3`

Now, to calculate the value of b, let's use the point (430, 150) in the equation (that is, x = 430 and C = 150):

`\begin{gathered} C=0.3x+b \\ (430,150)\colon \\ 150=0.3\cdot430+b \\ 150=129+b \\ b=150-129 \\ b=21 \end{gathered}`

Therefore the cost function is:

`C=0.3x+21`

B)

Now, to find the cost for 295 minutes, let's use x = 295 and calculate the value of C:

`\begin{gathered} C=0.3\cdot295+21 \\ C=88.5+21 \\ C=109.5 \end{gathered}`

Therefore the cost for 295 minutes is $109.50.