Question

a pool containing 21,400 gallons of water is being drained. the pool drains at a constant rate of 10 gallons per minute. consider function f, where f(x) represents the amount of water, in gallons, remaining in the pool after x minutes of draining.

• create function f.
• evaluate f(0) and explain what the solution means.

show your work or explain how you found your answer.

enter your answers and your work or explanation in the space provided.

Explanation:

Step1: Create the function

The initial amount of water is \(21400\) gallons and it drains at a rate of \(10\) gallons per minute. Using the linear function formula \(y = mx + b\) (where \(m\) is the slope and \(b\) is the \(y -\)intercept), here \(m=- 10\) (negative because the amount of water is decreasing) and \(b = 21400\). So the function \(f(x)=21400-10x\).

Step2: Evaluate \(f(0)\)

Substitute \(x = 0\) into the function \(f(x)\).

$$
LATEXBLOCK0
$$

When \(x = 0\) (i.e., at the start of the draining process, \(0\) minutes have passed), the value of \(f(0)\) represents the initial amount of water in the pool.

Answer:

• The function \(f(x)=21400 - 10x\).
• \(f(0)=21400\), which means that at the start (when \(0\) minutes of draining have occurred), there are \(21400\) gallons of water in the pool.