My guess is that you are taken advantage of Probably the teacher's cousin, who is a marine biologist, got this numbers from an actual experiment and thought, "Why don't I give this to the kids in my cousin's math class; let's see what they can figure out".
Seriously, I think what you did is right and the problem here is that data fluctuates a lot. Note, for example, that the intensity at 28 is greater that at 26. Also, the ratio of intensities at 20 and 22 is 1.11 while the ratio between 22 and 24 is 1.37.
I did plug the numbers in a spreadsheet and calculated K and B based on every pair of consecutive measurements. The standard deviation of B turned out to be 1212.0, while the average was 1854.3. This shows how wild the data is.
The best-fitting K and B computed by the LOGTEST function (OpenOffice 3.2) were -0,104 and 1458.159, respectively. OpenOffice uses linear regression (the "least squares" method). The average of K's and the median of B's computed from each pair were 0,1039
1468,741, which is pretty close.
Your solution probably should depend on what the question is testing. If you were studying the least squares method, then you should apply it. If you only studied the exponential function, then what you did is probably sufficient.
Disclaimer: I am not a statistician. You may get a more authoritative answer in one of the statistics forums on this site.