Suppose the average cost to community hospitals per patient per day in year is approximated by , where comtesponds te the year 2
Will the average cost per petient per day reach by 2024 ?
What is the value of in this case?

Ask by George Barber. in the United States

Jan 23,2025

Question

Suppose the average cost to community hospitals per patient per day in year is approximated by , where comtesponds te the year 2
Will the average cost per petient per day reach by 2024 ?
What is the value of in this case?

Ask by George Barber. in the United States

Jan 23,2025

UpStudy AI · Accepted Answer

To determine whether the average cost per patient per day will reach \$4,000 by 2024, we'll solve for the value of $$ x $$ in the given cost equation:

$$
\frac{72.469x^2 + 1353.5x + 2136}{x + 4} = 4000
$$

### Step-by-Step Solution:

1. **Set Up the Equation:**

$$
\frac{72.469x^2 + 1353.5x + 2136}{x + 4} = 4000
$$

2. **Multiply Both Sides by $$ x + 4 $$ to Eliminate the Denominator:**

$$
72.469x^2 + 1353.5x + 2136 = 4000(x + 4)
$$

3. **Expand the Right Side:**

$$
72.469x^2 + 1353.5x + 2136 = 4000x + 16000
$$

4. **Bring All Terms to One Side to Form a Quadratic Equation:**

$$
72.469x^2 + 1353.5x + 2136 - 4000x - 16000 = 0
$$

$$
72.469x^2 - 2646.5x - 13864 = 0
$$

5. **Apply the Quadratic Formula:**

$$
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
$$

Where:
- $$ a = 72.469 $$
- $$ b = -2646.5 $$
- $$ c = -13864 $$

6. **Calculate the Discriminant ($$ D $$):**

$$
D = (-2646.5)^2 - 4 \times 72.469 \times (-13864) = 11,022,803.114
$$

7. **Find the Square Root of the Discriminant:**

$$
\sqrt{D} \approx 3320.06
$$

8. **Solve for $$ x $$:**

$$
x = \frac{2646.5 + 3320.06}{2 \times 72.469} \approx \frac{5966.56}{144.938} \approx 41.15
$$

Since $$ x $$ typically represents whole years in this context, we can round $$ x $$ to the nearest whole number:

$$
x \approx 41
$$

### Conclusion:

**The value of $$ x $$ when the average cost per patient per day reaches \$4,000 is approximately 41.**

$$
x = \boxed{41}
$$
The average cost per patient per day will reach \$4,000 when $$ x = 41 $$.

Suppose the average cost to community hospitals per patient per day in year is approximated by , where comtesponds te the year 2
Will the average cost per petient per day reach by 2024 ?
What is the value of in this case?

Upstudy AI Solution

Answer

Solution

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Suppose the average cost to community hospitals per patient per day in year is approximated by , where comtesponds te the year 2 Will the average cost per petient per day reach by 2024 ? What is the value of in this case?

Upstudy AI Solution

Answer

Solution

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Latest Algebra Questions

Suppose the average cost to community hospitals per patient per day in year is approximated by , where comtesponds te the year 2
Will the average cost per petient per day reach by 2024 ?
What is the value of in this case?