2. Hurricanes are some of the largest storms on Earth. They are very low-pressure areas with diameters of over 500 miles. The barometric air pressure in inches of mercury at a distance of x miles from the eye of a severe hurricane is modeled by the formula: f(x) = 0.48 ln(x + 1) + 27 a) Find f(0) and f(100), and interpret these numbers / results. b) Using Desmos or some other graph software, graph the function. Give a brief description of how air pressure changes as you move away from the eye of the hurricane. Remember, the output represents air pressure and the input, x, is distance from the eye of the hurricane. c) Using the graph, at about what distance from the eye of the hurricane is the air pressure 28 inches of mercury?
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Find f(0) and f(100): f(0) = 0.48 * ln(0 + 1) + 27 = 0.48 * ln(1) + 27 = 0 + 27 = 27 inches of mercury f(100) = 0.48 * ln(100 + 1) + 27 ≈ 0.48 * ln(101) + 27 ≈ 30.34 inches of mercury Interpretation: At the eye of the hurricane (x = 0), the air pressure is 27 Show more…
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Hurricanes are one of nature's most destructive forces. These low-pressure areas often have diameters of over 500 miles. The function $f(x)=0.48 \ln (x+1)+27$ models the barometric air pressure, $f(x),$ in inches of mercury, at a distance of $x$ miles from the eye of a hurricane. Use this function to solve. Use an equation to answer this question: How far from the eye of a hurricane is the barometric air pressure 29 inches of mercury? Use the TRACE and ZOOM features or the intersect command of your graphing utility to verify your answer.
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20. Hurricanes The following data represent the atmospheric pressure p (in millibars) and the wind speed w (in knots) measured during various tropical systems in the Atlantic Ocean: Atmospheric Pressure (millibars), p: 993, 994, 997, 1003, 1004, 1000, 994, 942, 1006, 942, 986, 983, 940, 966, 982 Wind Speed (knots), w: 50, 60, 45, 45, 40, 55, 55, 105, 40, 120, 50, 70, 120, 100, 55 Source: National Hurricane Center (a) Use a graphing utility to draw a scatter diagram of the data, treating atmospheric pressure as the independent variable. (b) Use a graphing utility to find the line of best fit that models the relation between atmospheric pressure and wind speed. Express the model using function notation. (c) Interpret the slope. (d) Predict the wind speed of a tropical storm if the atmospheric pressure measures 990 millibars. (e) What is the atmospheric pressure of a hurricane if the wind speed is 85 knots?
Donna D.
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