i need help with the attached below please

MHF4U Assignment Lesson 17 Modelling Functions 1. A player hits a baseball into the air. A motion detector is used to gather data about the height of the ball. The resulting data is recorded in the table. Find the finite differences. Decide whether the data can be modelled by a linear, a quadratic, a cubic, or a quartic function. Then use the appropriate regression to determine the algebraic model for the data. DATA TABLE Time (s) 0 1 2 3 4 5 6 7 Height (m) First Differences 0.5 30.6 50.9 61.4 62.1 53.0 34.1 5.4 What model is the best fit for this data? How do you know?? Equation for the curve of best fit: Second Differences Third Differences Fourth Differences 2. The table describes the cooling of a cup of coffee as it sits out after being poured. DATA TABLE Time (min) 0 1 2 3 4 8 12 16 20 Temperature First Differences (Degrees Celsius) 55 52.8 50.7 48.7 46.7 39.7 33.7 28.6 24.3 Second Differences Common Ratio (round to two decimal places) What model is the best fit for this data? How do you know?? Equation for the curve of best fit: After how many minutes will the coffee be approximately 18 degrees? Explain your answer. 3. During a normal 5 second respiratory cycle in which a person inhales and then exhales, the volume of air in a person's lungs can be modelled by () = 0.027 3 0.27 2 + 0.675, where volume, V, is in litres and t is the time in seconds. In this cycle, when is the volume of air in the lungs more than 0.4L? Explain your