We recently held exams for the students. Consider the following:
I added a part c, asking (as I have on every single test so far this year) what a "reasonable domain" is for the problem.
The students can demonstrate that they know which variable is the independent variable and that negative numbers are unacceptable when the variable is months (or time in general).
That's all I look for - something that says "t > 0." If I see that or anything close, they get full credit. However, I have some students that add their creativity to the problem and it makes me smile. I thought I'd share with you two of my personal favorites.
"0 < t < 50 because then she gets married."
"0 < t < 700. <- This is 58 years later, so she would probably not live this long. If she did, I'd like to meet her to know how she lived so long and to get some of her money."
The first response is from a Burmese refugee that's only been at the school for one year, I think. The second is from an intelligent freshman who, I'm convinced, needs a special test that actually challenges him. (He also got the extra credit question of defining "defenestrate" by dissecting its Latin (Greek?) origin.)
((It means to throw out a window. It's one of my favorite words.)) (((I like to use it in story problems.)))