Questionof 8 VVS: 30-2 A5 21/22 Sem
Each year, a baseball team sells boxes of chocolates as a fundraiser to lower the cost of team fees. The price of the chocolates and the number of boxes sold varies each year. The information from five years of sales is given in the table below. \begin{tabular}{|c|c|c|c|c|c|} \hline \begin{tabular}{c} Price per \\ box (\) \end{tabular} & 3.00 & 4.00 & 5.50 & 6.50 & 8.00 \\ \hline \begin{tabular}{c} Boxes \\ sold \end{tabular} & 5837 & 3571 & 1950 & 1409 & 1118 \\ \hline \end{tabular} a. Find the regression equation in the form y=a x^{3}+b x^{2}+c x+d$that best approximates the data. Express the values of$a, b, c$, and$d$to the nearest hundredth. (1 mark) b. Use the equation to find the number of boxes, to the nearest whole number, that the team will sell if they charge$\$4.35$ per box. ( 1 mark) c. One year, the team only sold 366 boxes of chocolates. What price did they charge for each box? (1 mark) d. If the team raises the price too high, they will not sell any boxes. Use your regression equation to predict the lowest price of a box that will result in zero boxes sold. (1 mark)