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The image shows a problem involving **U.S. education funding** across several years with a focus on creating a **quadratic model**. Here is the summary of the task based on the image:

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### Problem Summary:
- The table provided shows discretionary funding for 3 specific years (2013, 2017, and 2019) in **billions of dollars**. The variable \( t \) represents the year since 2010, i.e., 
  - \( t = 3 \) corresponds to **2013**,
  - \( t = 7 \) corresponds to **2017**,
  - \( t = 10 \) corresponds to **2019**.

- The table entries are:
  \[
  \begin{aligned}
  t = 3 & \quad \text{Spending} = 73.27 \, \text{billion} \\
  t = 7 & \quad \text{Spending} = 72.81 \, \text{billion} \\
  t = 10 & \quad \text{Spending} = 70.93 \, \text{billion}
  \end{aligned}
  \]

The question asks you to:
1. **Find a quadratic model** \( p(t) = at^2 + bt + c \) that fits these data points.
2. Use this model to estimate **funding in 2019**.
3. Compare your estimate with the actual value from the table (which is **70.93 billion**).

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### Step-by-Step Solution:

#### 1. Set up the system of equations:
Since \( p(t) = at^2 + bt + c \), we substitute the given points \( (t, p(t)) \) to form three equations.

- At \( t = 3 \), \( p(3) = 73.27 \):
  \[
  9a + 3b + c = 73.27
  \]

- At \( t = 7 \), \( p(7) = 72.81 \):
  \[
  49a + 7b + c = 72.81
  \]

- At \( t = 10 \), \( p(10) = 70.93 \):
  \[
  100a + 10b + c = 70.93
  \]

#### 2. Solve the system of equations:
We have the following system:
\[
\begin{aligned}
9a + 3b + c &= 73.27 \\
49a + 7b + c &= 72.81 \\
100a + 10b + c &= 70.93
\end{aligned}
\]
We can solve this system to find the coefficients \( a \), \( b \), and \( c \).

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#### 3. Estimate Funding for 2019:
After determining the quadratic model, we will substitute \( t = 9 \) (since 2019 corresponds to \( t = 9 \)) to estimate the value of funding in 2019.

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Would you like me to proceed with solving the system of equations for the coefficients? Alternatively, I can guide you step-by-step through the calculations. Let me know!

The table shows U.S. education funding across several years, and the task involves finding a quadratic model for the funding data and predicting future funding amounts. The given data points are for 2013, 2017, and 2019. The quadratic model will help estimate funding in 2019.

Learn how to create a quadratic model for U.S. education funding using data points from 2013, 2017, and 2019. This problem involves building a quadratic equation system to estimate future funding, ideal for students in Grades 9-12.

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