1. Halley's Law states that the barometric pressure p(x) in inches of mercury at x miles above sea level is given by: p(x) = 29.92e -0.2x for x 2 0 Find the barometric pressure a) at sea level b) atop Mount Kanchenjunga (which is 8,586 meters above sea level). c) atop Mount Hunter (which is 14,573 feet above sea level). 2. A pie comes out of an oven at 350 . F and is placed to cool in a 80 . F kitchen. The temperature of the pie P (in . F) after t minutes is given by P = 80 + 270 e -0.017t. The pie is cool enough to cut when its temperature reaches 125 F. Determine the time this will take. Round to the nearest minute.3. Blood Pressure. The function P(t) = - 40 cos (2tit) + 120 approximates the blood pressure P in millimeters of mercury at time t in seconds for a person after moderate exercise. a) Find the time for one full heartbeat cycle. (This is the period.) b) Find the number of cycles (heartbeats) per minute. c) Graph only one wave of the blood pressure function. (Clearly specify its amplitude, period, range, max value and min value. Label axes to show 5 equally spaced significant points including start, middle, and end of wave.) 4. A radioactive isotope of plutonium, Pu-238, is used to make thermoelectric power sources for spacecraft. The half-life of Pu-238 is 87.7 years. A space probe was launched in 2020 with 4.0 kg of Pu-238. a) Use the half-life to determine the k value (round to 4 decimal places) for a function of the form Q(t) = Qo e - kt to model the quantity Q(t) of Pu-238 that is left t years after the launch in 2020. b) If 1.6 kg of Pu-238 is required to power the spacecraft's data transmitter, for how long after launch would scientists be able to retrieve data? (Show your equation and work. Round answer to the nearest year.) Systems