Answer all the questions, reference is right there btw.

2 35 45 Number of Cones 14 57 46 2. The table gives the number of ice cream cones sold by a food vendor. On the initial day (t=0 ) when the vendor added ice cream cones to the menu, the vendor sold 14 ice cream cones. Thirty-five days later (t=35), the vendor sold 57 ice cream cones. Ten days after that (t = 45), the vendor sold 46 ice cream cones. The number of ice cream cones sold can be modeled by the quadratic function I given by I(t) = at2 +bt+c, where I(t) is the number of ice cream cones sold on day t. (A) (i) Use the given data to write three equations that can be used to find the values for constants a, b, and c in the expression for I(t). (ii) Find the values for a, b, and c as decimal approximations. (B) (i) Use the given data to find the average rate of change of the number of ice cream cones sold, in cones per day, from t=35 to t = 45 days. Express your answer as a decimal approximation. Show the computations that lead to your answer. (ii) Use the average rate of change found in (i) to estimate the number of ice cream cones sold on day t= 40. Show the work that leads to your answer. (iii) Compare the estimate found in (ii) to the value given by the model, I(40). Using characteristics of the average rate of change and characteristics of the quadratic model, explain why the two estimates differ. (x)3 /bidenal anonismtxouggs lamboob en s. 10 soulov fle bria () (8) (C) Explain how the range values of the function I should be limited by the context of the problem. itall's to nouiston frauinmadtom