A dairy company's records reveal that it costs approximately C(w) = 3250.24 + 73.96 In w dollars for the company to produce w thousand gallons of whole milk each week. The company has been increasing production regularly since opening a new production plant five years ago and plans to continue the same trend of increases over the next ten years. The table shows actual and projected production of whole milk given the number of years since production began at the new plant. Weekly Production of Whole Milk Production Year (thousand gallons) 1 5.8 4 7.4 7 12.2 10 20.2 13 31.4 (a) Find the function for the quadratic model that gives production of whole milk in thousand gallons each week, where t is the number of years since production began at the new plant, with data from 1 s t s 13. (Round all numerical values to three decimal places.) w(t) = thousand gallons (b) Use the company's cost model along with the production model to write an expression modeling weekly cost as a function of time. (Round all numerical values to three decimal places.) C(w(t)) = dollars (c) Write the rate-of-change function of the cost function found in part (b). (Round all numerical values to three decimal places.) dc dt dollars per year (d) Estimate the company's weekly costs 4 and 8 years from now. (Round your answers to two decimal places.) 4 years from now $ 8 years from now $ Estimate the rates of change for those same years. (Round your answer to two decimal places.) 4 years from now $ per year 8 years from now $ per year