Question

Gina opens a small store. Each day her store is open, her profit increases by approximately $500.00.

Part A: Construct a function that BEST represents the estimated total profit after x days. Explain the type of function you created and why.

Part B: What number belongs in the blank space to complete Gina's function?

Part C: Explain the type of function Gina created and why that is the best type of function to represent the total profit k days after her newspaper advertisement is placed.

Answer 1

The linear function P(x) = 500x best represents the estimated total profits after x days. It's linear because the profit increases by a constant rate each day, and there's no need for an additional number in the function. Gina's function assumes a constant profit increase after a newspaper advertisement, which is why a linear function is suitable.

Step-by-step explanation:

The student's question pertains to the creation of a linear function that represents Gina's estimated total profits after x days. Part A: The function that best represents this is P(x) = 500x, where P(x) represents the total profit and x is the number of days the store has been open. This is a linear function because the profit increases by a constant amount each day.

Part B: The function is complete as is, so there is no need for a blank space to be filled.

Part C: The function created by Gina is also a linear function since it's based on the assumption that her daily profits increase at a constant rate after placing a newspaper advertisement. The linear relationship is the most suitable representation as it directly correlates the number of days passed with the consistent increase in profit.