Find the rate of change (slope) of cost per billable hour...

Question

The cost for tuition was at $106 per credit for in-county residents. An in-county student, Joan, taking 12 billable hours paid a total of $1586 to the bursar. Another in-county student, Bill, taking 7 billable hours paid a total of $946. There are other charges that are assessed by the school.

Find the rate of change (slope) of cost per billable hour. Is the answer you received the value you expected? Explain.

Answer 1

Firstly we can transcribe some of the information here into two ordered pairs/points which i will call

p0 = (7, 946)

p1 = (12, 1586)

where for any point p = (x, y), the x is the credit hours billable and y is the total $$ paid by the student p.

From these two points given we can determine the slope of a line with the following formula

slope = (y_final - y_initial) / (x_final - x_initial)

in other words the difference in price rise divided by the difference in credits taken.

*be sure to verify that this is a valid formula / the reasoning behind its use

Now, plugging in our values for p1 being the final, and p0 the initial point then we get,

slope = (1586 - 946) / (12 - 7) = 640 / 5 = 128 $ per credit hour.

Interestingly, this value is higher than the expected slope of 106$ per credit hour that we expected. You should try to think what the source of this discrepancy could be from...

One possible source of the discrepancy could be that there is an additional fee with each class taken (the problem did state that, "there are other charges..."), an alternative could be that once over a certain number of credits a flat additional fee is charged. Now, in this second possibility what could be possible credit hour values for this threshold? If it is indeed the case that this threshold rule is what is causing the discrepancy then is our calculation for the slope still valid? If not, how can can we modify our approach? These are questions for you to ponder further.

Answer 2

m \ (1585 - 946) / (12 - 7)