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Be sure to show all work neatly. You may handwrite or type your answers, Modeling Data: 1. The table shows the sales y (in millions of dollars) for PetSmart from 2008 to 2013 , where t is the year, with t=8 corresponding to 2008. (Source: PetSmart, Inc.) a. Use a graphing utility to find a cubic model for the sales, y(t) of PetSmart. b. Find the first and second derivatives of the function. c. Show mathematically that the sales of PetSmart were increasing from 2008 to 2013 using what you have learned in the course in Chapters 1 and 2. d. Find the year when the sales were increasing at the greatest rate by solving y(t)=0. 2. Now repeat the steps for the following updated data. a. Use a graphing utility to find a cubic model for the sales, y(t) of PetSmart. b. Find the first and second derivatives of the function. c. Were the sales of PetSmart increasing from 2016 to 2021? Show when sales were increasing or decreasing using what you have learned in the course in Chapters 1 and 2. d. Find the year when the sales were increasing at the greatest rate by solving y(t)=0 3. Use each model to predict the Sales in 2014 and 2015. Do a search to find the actual Sales for one or both years. Which model was most accurate? What happened in 2014/2015 that made a significant change in the revenue for PetSmart at that time

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