i). To build up enough equity in your new home, the rule of thumb is to stay there for at least five years; and on the average the expected length of stay in a single family home is 11.5 years for first-time home buyers and 15 years for buyers who have owned homes before. Radon is a radioactive gas found in homes in the US and comes from breakdown of uranium in soil, rock and water. The gas, which can be harmful in large amounts over long exposure times, moves up from underground into homes through cracks and holes in the foundation. If a home had 5 grams radon (half-life =3.8 days), and its rate of decay is proportional to the amount present, how much radon would you estimate to be present after living in the house for: a). One day b). One year c). 10 years ii). Find the air pressure P(x) at a cruising altitude of 35,000 feet if the rate of change of pressure with height P(x) is proportional to the pressure. Assume that at a height of 18,000ft. the pressure is half its value at sea level (x=0) where at x=0 the pressure is P0