EGET 3171

EGET 3171

Differential Equations & Partial Derivatives

1. Carbon-12, one of the 3 isotopes of carbon, is radioactive and decays at a rate proportional to the amount present. Its half life is 5730 years (that is, it takes 5730 years for a given amount to decay to half its original size).  If 10 grams were present originally, how much will be left after 2000 years? [7.85 grams]


2. Under normal conditions, the rate of bacteria in a given sample grows at a rate proportional to the number present. In a certain sample, there were 105 present at a given time, and there were 3 times that present after 10 hours. How many were present after 20 hours? [9 x 105]


3. Find any relative minimum, maximum or saddle points of the equation:

                                    z = 3x – x2