Mathematics Problems:

We can make some interesting mathematics problems by taking some information from the actual situation and making some simplifying assumptions to make the problems solvable on a reasonable amount of time

- The well is leaking 5,000 barrels of oil per day (Thought to be true initially, but later raised a great deal)
- The well is located about 5 miles from the coast (True)
- The oil will form a circle as it reaches the surface of the water. (Not True)
- The oil slick will have a consistent thickness of 100 µm (micrometres) (Not True)

- Please find the radius of the spill after 1 day,2 days,3 days,4 days,5 days,10 days, and 20 days. (Do each calculation by first finding the volume of the oil released, then finding the radius of the cylinder 100µm thick that contains that much oil.
- Find an explicit equation that gives the radius of the oil slick as a function of time.
- Please graph the radius of the spill as a function of time.
- Please estimate how long it will take the spill to reach the coast.
- Write a clear explanation of why the volume of the oil and the radius of the slick are not directly proportional.

Has anyone produced the graph in #3 yet?

ReplyDeleteYes...most of my students are able to build a function of this type and graph it. The two big weaknesses this problem brought out for many of my students were:

ReplyDelete1) keeping track of the different units and changing to ocnsistent units, and

2) the concept that radius and volume are not directly proportional. Students have a knee jerk reaction to want to say that once they find the radius after 1 day, the radius for 5 days will be five times the first answer. In this way the problem is a great precursor to the related rates problems that will arise in calculus.