Question

A store is monitoring the sale price of an item. The table models the daily price, y, in dollars, after a given number of days, x. x (days)01234 y (price in dollars)15013512010590 Part A: What type of function best models the data

Answer 1

The data provided by the student, showing a constant rate of change in price over several days, indicates that a linear function models the data best, with an equation of y = -15x + 150.

Step-by-step explanation:

The student is asking about the identification of a function type that best models a data set dealing with the daily price of an item over several days. The data shows a consistent decrease in the item's price as the days go by. Given the data points x (days) as 0, 1, 2, 3, 4 and y (price in dollars) as 150, 135, 120, 105, 90, we can notice that for each increase in one day, the price decreases by 15 dollars. This is a constant rate of change, which indicates a linear function is the most appropriate model for this data set.

Specifically, the linear function can be described as y = mx + b, where m is the slope (rate of change) and b is the y-intercept (the starting value when x is 0). In this case, the slope m is -15 (since the price drops by 15 dollars per day), and the y-intercept b is 150 (the price of the item on day 0). Therefore, the linear equation modeling the data is y = -15x + 150.