The normal daily maximum temperature T (in degrees Fahrenheit) for Denver, Colorado, is shown in the table below. Month Temperature Month Temperature a. Graph the data. b. Use your calculator to find a regression equation of the form y=a*sin(bx+c)+d Jan Feb Mar Apr May Jun 43.2 46.6 52.2 61.8 70.8 81.4 Jul Aug Sep Oct Nov Dec 88.2 85.8 76.9 66.3 52.5 44.5 c. Graph the regression equation and the data. How well does the regression equation fit the data? d. What is the period of the regression equation? Does it make sense? e. What is the amplitude of the regression equation? What does it mean in terms of the problem? f. Find and graph dy dx g. Based on the graph of the derivative, during what time does the temperature change most rapidly? Most slowly?

Planetary Velocity The following table gives the mean velocity of planets in their orbits versus their mean distance from the sun. Note that 1AU astronomical unit is the mean distance from Earth to the sun, abut 93 million miles. Planet d=distance AU v=velocity km/sec Mercury 0.39 47.4 Venus 0.72 35.0 Earth 1.00 29.8 Mars 1.52 24.1 Jupiter 5.20 13.1 Saturn 9.58 9.7 Uranus 19.20 6.8 Neptune 30.05 5.4 Astronomers tell us that it is reasonable to model these data with a power function. a Use power regression to express velocity as a power function of distance from the sun. b Plot the data along with the regression equation. c An asteroid orbits at a mean distance of 3AU from the sun. According to the power model you found in part a, what is the mean orbital velocity of the asteroid?