The average weekly sales for a clothing store between 2004 and 2008 are given below. Average Weekly Sales for a Clothing Store Year Thousand Dollars 2004 38.85 2005 53.64 2006 63.78 2007 72.1 2008 68.03 (b) Align the input so that t = 0 in 2000. Find a function for quadratic model for the data that gives the average weekly sales for the clothing store in thousand dollars, with data from 4 ≤ t ≤ 8. (Round all numerical values to three decimal places.) s(t)=−2.835t2+41.693t−83.182   (c) Numerically estimate the derivative of the model from part (b) in 2007 to the nearest hundred dollars.  (BLANK)$ per year (d) Interpret the answer to part (c). In 2007, the average weekly sales for the clothing store were increasing by (BLANK) $ per year.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.