(Modeling Functions HC)

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, $x$.
\begin{tabular}{|c|l|l|l|l|l|}
\hline $\boldsymbol{x}$ (days) & 0 & 1 & 2 & 3 & 4 \\
\hline $\boldsymbol{y}$ (price in dollars) & 150 & 135 & 120 & 105 & 90 \\
\hline
\end{tabular}

Part A: What type of function best models the data? (5 points)

Part B: Explain how to determine the best model. Support your answer using complete sentences. (5 points)

Step 1 ：The problem is asking for the type of function that best models the data. Looking at the data, we can see that the price of the item decreases by $15 each day. This suggests that the relationship between the number of days and the price is linear. Therefore, a linear function would best model the data.

Step 2 ：To confirm this, we can calculate the rate of change between each pair of consecutive points. If the rate of change is constant, then the function is linear.

Step 3 ：The rates of change between each pair of consecutive points are all -15, which is constant. This confirms that the function is linear.

Step 4 ：The type of function that best models the data is a \(\boxed{\text{linear function}}\).