Questions: Use the table to answer the question. Find the rate of change. Time (minutes) Distance (miles) 3 36 5 60 7 84 9 108 11 132

Solution Steps

The table provides the following data points:

• At \( t = 3 \) minutes, \( d = 36 \) miles.
• At \( t = 5 \) minutes, \( d = 60 \) miles.
• At \( t = 7 \) minutes, \( d = 84 \) miles.
• At \( t = 9 \) minutes, \( d = 108 \) miles.
• At \( t = 11 \) minutes, \( d = 132 \) miles.

The rate of change (slope) is calculated using the formula: \[ \text{Rate of change} = \frac{\Delta d}{\Delta t} = \frac{d_2 - d_1}{t_2 - t_1} \] Using the first two data points: \[ \text{Rate of change} = \frac{60 - 36}{5 - 3} = \frac{24}{2} = 12 \, \text{miles per minute}. \]

To ensure consistency, calculate the rate of change using another pair of data points, such as \( t = 7 \) and \( t = 9 \): \[ \text{Rate of change} = \frac{108 - 84}{9 - 7} = \frac{24}{2} = 12 \, \text{miles per minute}. \] The rate of change is consistent across the data points.

Final Answer