Mia opens a coffee shop in the first week of January. The function W(x) = 0.002x3 - 0.01x2 models the total number of customers visiting the shop since it opened after x days. She then opens an ice cream parlor in the month of February. The function R(x) = x2 - 4x + 13 models the total number of customers visiting the parlor since it opened after x days. Which function represents the difference, D(x), in the number of customers visiting the two shops?D(x) = 0.002x3 + 1.01x2 - 4x + 13D(x) = 0.002x3 + 0.99x2 + 4x - 13D(x) = 0.002x3 - 1.01x2 + 4x - 13D(x) = 0.002x3 - 0.99x2 - 4x + 13
Accepted Solution
A:
We need to know the function that models the difference in the number of customers visiting the two stores. We know the function that models the number of customers in the cafeteria W (x) = 0.002x3 - 0.01x2 We also know the function that models the number of customers who visit the ice cream parlor R (x) = x2 - 4x + 13 Therefore the difference, D (x), in the number of customers visiting the two stores is: D (x) = W (x) - R (x) D (x) = 0.002x ^ 3 - 0.01x ^ 2 - (x ^ 2 -4x +13) D (x) = 0.002x ^ 3 - 0.01x ^ 2 - x ^ 2 + 4x -13
D (x) = 0.002x ^ 3 - 1.01x ^ 2 + 4x -13 The answer is the third option