Dr. Dawn's blog

Working together with my best friend since the 5th grade who is now a nurse practitioner, I developed this problem in which students have to use exponential decay (half life) to protect their patient from dangerous drug interactions.

Your patient has a fungal infection and is taking ketoconazole 400mg daily for 10 days. During this time they have been advised to stop taking their atorvastatin because of the potential for severe interaction. They may begin taking the atorvastatin again when the concentration of ketoconazole is at 12.5% of the original amount. The half life of ketoconazole is 8 hours.

How many hours after the last dose of ketoconazole can you patient resume taking the atorvastatin?

Here is a problem I have used in my algebra class. It uses knowledge of lines, functions, and extrapolation versus interpolation.  (I find that in order for the students to be able to read the picture of the sign, I have to print it in color.  Next time I go to the zoo I am going to try to get a better picture.)

The sign shown below from the Detroit Zoo gives various information about giraffes.  Use the information from the sign to answer the following questions.

A) Write a function g(t) describing the height of a giraffe during its first year of life where t is the age of the giraffe in months.

B) How tall is a giraffe when it is one year old?  Give your answer in a complete sentence with units.

C) Compute g(-1).  Is this interpolation, reasonable extrapolation, or reckless extrapolation?

I was so excited about New Horizon’s fly by of Pluto, that I decided to create some math problems about it.  Here they are.  The first one uses the concepts of percent change and volume of a sphere.  The second two use right triangle trigonometry.

1) Answer the question posed in @MathInTheNews ‘s tweet from July 14, 2015:
New Horizons says Pluto’s diameter is 1473mi, 50mi larger than believed. What % does that change its volume estimate?

(Yes, the picture was part of the tweet)

2) Pick two mountains in the large picture of Pluto.  The angle of elevation from the tip of the mountain’s shadow to the tip of the mountain is approximately y/736.5 radians where y is the distance in miles from the base of the mountain to the edge of Pluto in the picture.

a)  What is the height of each of your two mountains?

b) How precise do you think our method is?

c)  Do you think NASA’s claim that there are 11,000 ft high mountains on Pluto is credible?

(Note to other instructors, the estimation of the angle given above is very imprecise, so the students ended up finding mountain heights no more than 7,000 feet high.  In order to improve precision, I printed the following picture out as a 11 by 17 picture).

3) In a July 13, 2015 article for Reuter’s Irene Klotz wrote, “Mysterious Pluto looms large and turns out to be larger than expected as NASA’s New Horizons spacecraft wraps up a nearly decade-long journey, with a close flyby on track for Tuesday, scientists said on Monday.  The nuclear-powered probe was in position to pass dead center of a 60-by-90-mile (97-by-145 km) target zone between the orbits of Pluto and its primary moon, Charon, at 7:49 a.m. EDT (1149 GMT) on Tuesday, said managers at New Horizons mission control center, located at the Johns Hopkins University Applied Physics Laboratory outside of Baltimore. After a journey of 3 billion miles (4.88 billion km), threading that needle is like golfer in New York hitting a hole-in-one in Los Angeles, project manager Glen Fountain told reporters.”

Is this analogy correct?  (You will need to look up some additional numbers and make additional assumptions to answer this question).

Here’s a warm up activity to get students thinking mathematically and thinking about what math is:

One of my friends posted this picture on Facebook.  Use it and whatever other resources you need to answer the following questions.

a) Assuming the first statement is correct, is the second statement correct?

b)  What (if anything) is wrong with this “solution” to homelessness?

c) To what extent was this problem “doing math”?  Were both parts a and b math problems?

This is a problem I work through in my pre-calculus class when we are discussing the meaning of the slope and y-intercept.  It also gives me the opportunity to discuss the perils of extrapolating far outside of the data set.

Consider the following data and the linear model that fits it.

The equation for the linear model is y=0.019x+4.76.  Answer the following questions in complete sentences with units.

1. What are the units for the slope?
2. What does the slope mean in this particular situation?
3. What are the units for the y-intercept?
4. What does the y-intercept mean in this particular situation?

(data from http://www.esrl.noaa.gov/gmd/dv/data/index.php?site=mlo&parameter_name=Carbon%2BDioxide&frequency=Monthly%2BAverages and http://www.ncdc.noaa.gov/cag/ )

Randall Munroe drew a lovely comic strip graphing the effects of proximity to a cat on the human intellect:

(You can view it here: http://xkcd.com/231/).

In differential calculus I asked students to describe the graphs using their knowledge of calculus.  Statements about both the first and second derivative are expected.

In Intermediate Algebra here at UDM we study qualitative graphs, so I also asked my Algebra students to describe the graph.  These students have to say things like the intelligence of the human is decreasing, but at an ever faster rate.

One caution with this comic: some students do not know what “inanity” means, so I use this problem on the review sheet rather than the exam.

In this FoxTrot strip Paige has been cramming for her math final and thus is answering all questions in mathematical notation.

http://assets.amuniversal.com/b07d90305e30012ee3bf00163e41dd5b

(Its the May 22, 2005 strip, if the link doesn’t work.)

In precalculus I asked the students:

1) What temperature will it be tomorrow?  Is it going to be hot tomorrow?

(The answer is sin^{-1}(1) =90 degrees, so it will be hot).

2) What does the girl (Paige) want for snack?

(The answer is 3.14159265359…, so she wants pie).

In calculus of sequences and series, you could also ask what the discount was in the fourth panel, which requires computing the sum of an infinite geometric series.

In an algebra class one could ask what time Paige went to bed (\sqrt{121}= 11:00) or What is on TV? (4!=24).

Here are a few comic strips dealing with extrapolation.  Each is accompanied by a question I would ask students about the strip.

1) Explain this comic strip using knowledge from the course.

(This strip is by Randall Munroe and can be accessed at http://xkcd.com/605/)

2) Read this comic strip by Randal Munroe and answer the following questions.

(This strip can be accessed at http://xkcd.com/1007/)

a) For which span of years does the Munroe have data on the frequency of the use of the word “sustainable”?

b) Munroe made a model of this data.  Does the model fit the data well?

c) Munroe used his model to predict the frequency of the word “sustainable” in 2061.  What percent of words does he predict will be ”sustainable” in 2061?  Is this an example of interpolation or extrapolation?  Is this prediction likely to be valid?