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The table provided describes the number of parked cars in a mall as a function of time, using the equation:

\[
C(t) = -50t^2 + 430t + 310
\]

Here, \( C(t) \) represents the number of cars parked in the mall at time \( t \) hours after 8:00 a.m. The task is to complete the table by filling in the missing values for certain times \( t \).

Let me calculate the missing values using the given equation:

### Calculations for Missing Values:

1. **At \( t = 3 \) hours:**

\[
C(3) = -50(3)^2 + 430(3) + 310 = -50(9) + 1290 + 310 = -450 + 1290 + 310 = 1150
\]

So, \( C(3) = 1150 \).

2. **At \( t = 5 \) hours:**

\[
C(5) = -50(5)^2 + 430(5) + 310 = -50(25) + 2150 + 310 = -1250 + 2150 + 310 = 1210
\]

So, \( C(5) = 1210 \).

3. **At \( t = 8 \) hours:**

\[
C(8) = -50(8)^2 + 430(8) + 310 = -50(64) + 3440 + 310 = -3200 + 3440 + 310 = 550
\]

So, \( C(8) = 550 \).

### Completed Table:

| Time (Hours), \( t \) | Number, \( N \) | \( (t, N) \)  |
|---------------------|-----------------|--------------|
| 0                   | 310             | (0, 310)     |
| 1                   | 690             | (1, 690)     |
| 2                   | 970             | (2, 970)     |
| 3                   | 1150            | (3, 1150)    |
| 

Complete the table showing the number of cars parked in the mall over time using the equation C(t) = -50t^2 + 430t + 310.

Learn how to apply the quadratic equation C(t) = -50t^2 + 430t + 310 to calculate the number of cars parked at different hours after a mall opens. Detailed step-by-step solutions are provided. Suitable for high school students in Grades 9-12.

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