A grocery store manager decided to feature cases of soft drinks in the front of the store. He wanted to make certain that shoppers would not miss the sale, so he decided to have the cases stacked in a square-based pyramid; that is, each level was made up of a square number of cases. He did not want to haul any more cases than needed into the store but instead, would have stock brought in as needed to keep the pyramid several levels tall.

a. How many cases, C, of soft drinks are needed to create a square-based pyramid L level high? Determine the number of cases needed for several values of L.

b. To what function family do the data you found in part (a) belong? How do you know?

c. Determine an equation for C as a function of L.