This problem set is from a 200-level introductory undergraduate class. The students had no prerequisites except at least one semester of college-level science or math.

The students have already calculated the black body temperature for all the planets in the solar system, and they've also calculated the optical thickness of Earth's atmosphere on the previous problem set.

This problem set is one of the weekly problem sets given in the 12-week course.

Stefan-Boltzmann equation
greenhouse effect
albedo effect
radiocarbon dating

hypothesis testing

using math to address geological questions
making simple x-y graphs

The first problem in this assignment is the culmination of the unit on energy balance and greenhouse gases. The students have already calculated blackbody temperatures as a function of albedo, sun's luminosity and distance from sun. They have also already calculated the magnitude of the greenhouse effect (optical thickness) of the modern atmosphere. In this first problem, the students apply these same calculations to the Faint Young Sun hypothesis and infer what can account for the geological evidence for liquid water on earth since 4.3 Ga. The second problem follows an introductory lecture on radiometric decay and radiometric dating. The students have seen the decay equation and learned what are decay constants and stable versus radioactive isotopes. In this problem, the students apply these concepts to radiocarbon.

When grading this problem set, I check if the approach to the calculations was correct, and if the narrative interpretations of each step reveal that the student understood the implications of their calculations.