Questions: Harold wrote this equation to model the level of water in a pool over time. The variable x represents time in hours. f(x) = 3,500 - 225x Which statements about the situation are true? Check all that apply. The water level is rising. The water level is falling. The initial level of water in the pool was 3,500 units. The initial level of water in the pool was 225 units. The pool was empty after 14 hours. The water was 2,600 units high after 4 hours.

Solution Steps

To determine which statements are true, we need to analyze the given linear equation \( f(x) = 3,500 - 225x \). The coefficient of \( x \) indicates the rate of change of the water level. The constant term represents the initial water level. We can also calculate specific values of \( f(x) \) to verify the statements about the water level at certain times.

1. Water Level Change: The coefficient of \( x \) is \(-225\), which means the water level is falling by 225 units per hour.
2. Initial Water Level: The initial level of water, when \( x = 0 \), is 3,500 units.
3. Pool Empty Time: To find when the pool is empty, solve \( f(x) = 0 \).
4. Water Level at 4 Hours: Calculate \( f(4) \) to find the water level after 4 hours.

The function \( f(x) = 3500 - 225x \) indicates that the water level is decreasing over time since the coefficient of \( x \) is negative. Therefore, the water level is falling.

When \( x = 0 \), the initial water level is calculated as: \[ f(0) = 3500 - 225 \cdot 0 = 3500 \] Thus, the initial level of water in the pool was \( 3500 \) units.

To find when the pool is empty, we set \( f(x) = 0 \): \[ 0 = 3500 - 225x \implies 225x = 3500 \implies x = \frac{3500}{225} \approx 15.56 \] This means the pool will be empty after approximately \( 15.56 \) hours.

To find the water level after \( 4 \) hours, we calculate: \[ f(4) = 3500 - 225 \cdot 4 = 3500 - 900 = 2600 \] Thus, the water level is \( 2600 \) units after \( 4 \) hours.

Final Answer