Question

what is the rate of change of gareths distance from the bottom of the pool with respect to time, and what is his initial distance from the bottom?

rate of change = 0 feet per minute, and distance = 0 foot
rate of change = 12 feet per minute, and distance = 12 feet
rate of change = 12 feet per minute, and distance = 0 foot
rate of change = 0 feet per minute, and distance = 12 feet

Explanation:

Identify the initial distance from the y-intercept

$$ \text{initial distance} = y(0) = 12\text{ feet} $$

Calculate the rate of change from the slope of the horizontal line

$$ \text{rate of change} = \frac{12 - 12}{11 - 0} = 0\text{ feet per minute} $$

Answer:

• rate of change = 0 feet per minute, and distance = 0 foot
• rate of change = 12 feet per minute, and distance = 12 feet
• rate of change = 12 feet per minute, and distance = 0 foot
• rate of change = 0 feet per minute, and distance = 12 feet (Correct answer)