Question: In 2009, a study was done on the impact of sea level rise in the mid-Atlantic states.20 Let a(t) be the depth of the sea in millimeters (mm) at a typical point on the Atlantic Coast, and let m(t) be the depth of the sea in mm at a typical point on the Gulf of Mexico, with time t in years since data collection started.
(a) The study reports "Sea level is rising and there is evidence that the rate is accelerating." What does this statement tell us about a(t) and m(t)?
(b) The study also reports "The Atlantic Coast and the Gulf of Mexico experience higher rates of sea-level rise (2 to 4 mm per year and 2 to 10 mm per year, respectively) than the current global average (1.7 mm per year)." What does this tell us about a(t) and m(t)?
(c) Assume the rate at which the sea level rises on the Atlantic Coast and the Gulf of Mexico are constant for a century and within the ranges given in the report.
(i) What is the largest amount the sea could rise on the Atlantic Coast during a century? Your answer should be a range of values.
(ii) What is the shortest amount of time in which the sea level in the Gulf of Mexico could rise 1 meter?