The function C(q)=22400-2800q represents the balance in your college payment account after q quarters. 

Interpret the Slope in this situation.

The balance in this account is Select an answer increasing decreasing  at a rate of  Select an answer dollars quarters per dollar years dollars per quarter dollars per year quarters 

Interpret the Initial Value in this situation.

After  quarters, the balance in this account is $.

How many quarters will this account pay for?

You can pay for  quarters before the money in this account is gone.

Let's analyze the given function $ C(q) = 22400 - 2800q $, where $ C(q) $ represents the balance in your college payment account after $ q $ quarters.

### 1. **Interpretation of the Slope**
The slope of the function is given by the coefficient of $ q $, which is $-2800$. This indicates how the balance changes per quarter.

- The slope is **negative**, so the balance is **decreasing**.
- The slope is $-2800$, meaning that the balance is **decreasing by $2800 per quarter**.

Thus, the interpretation is:  
The balance in this account is **decreasing** at a rate of **2800 dollars per quarter**.

### 2. **Interpretation of the Initial Value**
The initial value is the constant term in the function, which is **22400**. This represents the balance in the account when $ q = 0 $ (i.e., before any payments are made).

So, after **0 quarters**, the balance in this account is **$22400**.

### 3. **How many quarters will this account pay for?**
To find how many quarters this account will cover before the balance reaches 0, we set $ C(q) = 0 $ and solve for $ q $:

\[
22400 - 2800q = 0
\]

Solve for $ q $:

\[
2800q = 22400
\]

\[
q = \frac{22400}{2800} = 8
\]

Therefore, you can pay for **8 quarters** before the money in the account is gone.

### Summary:
- The balance in the account is **decreasing** at a rate of **2800 dollars per quarter**.
- The initial balance is **$22400**.
- You can pay for **8 quarters** before the money is gone.

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Do you have any questions, or would you like more details on any part?

Here are some related questions to explore further:
1. How does the slope affect the total number of quarters the account can cover?
2. What would happen if the rate of decrease was slower (e.g., $2000 per quarter)?
3. How would the function change if the initial balance was $30,000 instead of $22,400?
4. How could the account be extended to cover more quarters?
5. What is the balance after 4 quarters, based on this function?

**Tip:** In any linear equation, the slope represents how much the dependent variable changes per unit increase in the independent variable.

The function C(q)=22400-2800q represents the balance in your college payment account after q quarters. Interpret the Slope in this situation. The balance in this account is Select an answer increasing decreasing at a rate of Select an answer dollars quarters per dollar years dollars per quarter dollars per year quarters. Interpret the Initial Value in this situation. After quarters, the balance in this account is $. How many quarters will this account pay for? You can pay for quarters before the money in this account is gone.

Explore how to interpret the slope and initial value in the linear function C(q) = 22400 - 2800q, which represents a college payment account balance. Understand how the balance decreases by $2800 per quarter and how many quarters the account will cover before running out. Suitable for students in Grades 9-10.

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