Suppose the average cost to community hospitals per patient per day in year \( x \) is approximated by \( \frac{72.469 x^{2}+1353.5 x+2136 s}{x+4} \), where \( x=11 \) comtesponds te the year 2 Will the average cost per petient per day reach \( \$ 4000 \) by 2024 ? What is the value of \( x \) in this case? \( x=\square \)

To determine whether the average cost per patient per day will reach $4000 by 2024, we first need to find the value of \( x \) that corresponds to 2024. Since \( x = 11 \) refers to the year 2012 (2 years after the base year 2010), we can find \( x \) for 2024 by calculating: 2024 - 2010 = 14, which gives \( x = 14 \). Now, we substitute \( x = 14 \) into the cost function: \[ \text{Cost} = \frac{72.469 \cdot 14^{2} + 1353.5 \cdot 14 + 2136 s}{14 + 4} \] Calculating this will provide the average cost. So, to find out whether it will reach $4000, you plug in the value of \( x \) as 14 and evaluate the expression! Exploring the trends in healthcare spending can often reveal surprising insights, and keeping an eye on such projections can lead to better budgetary decisions! Plus, healthcare costs are always evolving, just like technology! Hang tight while you crunch those numbers!