## Sea Level Rise Related Rates Problem

This is a problem I normally give at the end of semester in calculus 1 as part of a worksheet composed entirely of application problems from various sections of the book (Some of the other problems from this worksheet appear else where in the blog. Links to them are at the bottom of this post). This kind of mixed review can be very powerful because the students have to figure out which of the many techniques they have learned apply to the situation. This is a skill that employers recruiting at our university’s career fairs have told me the are seeking. I include the references on the worksheet that I hand out, not just the questions.

A variation on this problem (using function composition and similar triangles instead of related rates) is suitable for use in a precalculus course. The precalculus variation will be appearing as [4].

Here’s the problem:

(Hint: In this problem you need to be very careful with units). The Maldives is an example of a poor low-lying country which will be hit soon and hard by the effects of global climate change including sea level rise [3], [2]. The Maldives is located south-southwest of India. It consists of approximately 1,190 islands and is the lwest country in the world with a maximum elevation of 2.4 m. The Maldives has a total area of 298 km squared and a coastline of 644km [2]. Since the actual shape of the Maldives is complicated, we will use a simpler shape to compute with and assume this is a good stand-in for the real islands. We will pretend the nation is one triangular prism as pictured below. The width of the base is 1 km and the length of the base is 320 km. The height of the prism is 2.4m.

a) Convert all units to kilometers and label the picture with the measurements in kilometers. What is the map area of the prism in kilometers squared? By map area, in this problem, we mean the area of the rectangle you would see by looking down on the prism from above.

b) At what rate is the area changing when the elevation is 2meters if the sea level is rising at a rate of 4.3325 mm per year?

c) The Intergovernmental Panel on Climate Change (IPCC) predicts between 0.28 and 0.98 m of sea level rise by 2100 [1]. Some reputable sources predict up to 2 m of sea level rise by 2100 [3]. What is the annual rate of sea level rise in mm per year for each of these estimates? What is the rate of change of the area for each of these estimates?

References

[1] J. A. Church, et. al. “Sea Level Change“. In: *Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change*. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA. 2013.

Full text available at http://www.climatechange2013.org/images/report/WG1AR5\_Chapter13\_FINAL.pdf

[2] The CIA World Factbook, https://www.cia.gov/library/publications/the-world-factbook/geos/mv.html, accessed on May 6, 2015.

[3] K. Dow and T. E. Downing, *The Atlas of Climate Change: Mapping the world’s greatest challenge*, 3rd ed.

University of California Press, Berkeley, 2011.

[4] Archey, Dawn. “Sea Level Change and Function Composition.” *In Mathematics and Social Justice Modules for the Classroom*. Eds. Karaali, Gizem and Khadjavi, Lily. to appear.

Other problems in the Calculus 1 mixed review worksheet included:

https://sites.udmercy.edu/archeyde/2015/04/13/limits-and-fairy-tales/