Astronomy final exam question: Drake equation

Astronomy 210 Final Exam, Spring Semester 2009
Cuesta College, San Luis Obispo, CA

[20 points.] Describe in words what the Drake equation is, and explain why it is able to give very different results.

Solution and grading rubric:

• p = 20/20:
  Correct. Drake equation allows an estimate for the number of advanced technological civilizations in the Milky Way to be calculated based on the approximate number of lifezone planets, multiplied by the wildly speculative probability of life arising and evolving into an advanced technological society. The latter part of the Drake equation is based on untestable numbers, and thus vastly different results can be obtained by putting vastly different assumptions.
  
• r = 16/20:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
  
• t = 12/20:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors.
  
• v = 8/20:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
  
• x = 4/20:
  Implementation/application of ideas, but credit given for effort rather than merit.
  
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:
Section 30674
p: 15 students
r: 2 students
t: 3 students
v: 6 students
x: 1 student
y: 3 students
z: 1 student

A sample "p" response (from student 2286), also making a connection to a Star Trek reference:

A sample "r" response (from student 1801), who at least remembers what the Drake equation is supposed to quantify, and the relevant factors:

A sample "t" response (from student 9898), forgetting what the Drake equation is, but at least argues why the Drake equation can have widely varying results:

A sample "v" response (from student 2537), who also name-checks Star Trek, but is not quite able to explain what the Drake equation is supposed to quantify, and why it can give widely varying results, while mentioning some possible determining factors:

A sample "y" response (from student 1959), incorporating a visual pun into a rebus: