(a) Find the cubic polynomial that best fits the data. (Round a|I coefcients to three decimal places.) m = .002x3 + .1045.~.r2 + 1.9663: + 2.456 I (b) Draw a graph of the polynomial from part (a) together with a scatter plot of the data. Y I 5 10 15 20 25 30 5 10 15 20 25 30 I I I I I I I I . I I . I I x I I I I I I x 5 10 15 20 25 30 5 10 15 20 25 30 (c) Use your result from part (b) to estimate the number of vegetables that subjects would be able to name in 4-5 seconds. (Round your answer to the nearest whok (d) According to the model, how long (to the nearest 0.1 second] would it take a person to name six vegetables? 3:: The radiation energy E emitted by a heated surface (per unit surface area) is directly proportional to the fourth power of the absolute temperature 7 of the surface. (a) Express this relationship by writing an equation. (Use k as the constant of proportionality.) (b) The temperature is 6000 K at the surface of the sun and 500 K at the surface of planet Y. How many times more radiation energy per unit area is produced by the sun than by planet Y? times moreEvery one of us is all too familiar with the phenomenon of forgetting. Facts that we clearly understood at the time we first learned them sometimes fade from our memory by the time the final exam rolls around. Psychologists have proposed several ways to model this process. To develop her own model, a psychologist performs an experiment on a group of volunteers by asking them to memorize a list of 100 related words. She then tests how many of these words they can recall after various periods of time. The average results for the group are shown in the table. Time Words recalled 15 min 60.3 1 h 41.1 33.3 1 day 28.8 2 days 22.9 3 days 21.6 5 days 18.9 (a) Use a graphing calculator to find a power function of the form y = at" that models the average number of words y that the volunteers remember after t hours. (Round all values to three decimal places.) y 25.964f-125 X Find an exponential function of the form y = ab to model the data. (Round all values to three decimal places.) y : 23.443 . 1.0517 X