Question

(02.03 hc)
the following table shows the amount of water leaking from an inflatable pool as a function of time:
find and interpret the meaning of the x - intercept in this scenario.
(7,0), the time it takes to empty the water in the pool
(5,0); the time it takes to empty the water in the pool
(5,0); the time it takes to fill up the water in the pool
(7,0), the time it takes to fill up the water in the pool

Explanation:

Step1: Find the linear function

The general form of a linear function is \(y = mx + b\). Using the points \((0,35)\) (so \(b = 35\)) and \((1,30)\), the slope \(m=\frac{30 - 35}{1-0}=- 5\). So the function is \(f(x)=-5x + 35\).

Step2: Find the x - intercept

Set \(f(x)=0\), then \(0=-5x + 35\). Solve for \(x\):
\(5x=35\), \(x = 7\). The x - intercept is \((7,0)\).

Step3: Interpret the x - intercept

In this context, \(x\) is time (in minutes) and \(f(x)\) is the amount of water (in liters). When \(f(x) = 0\) (water is empty), \(x = 7\) means the time it takes to empty the water in the pool.

Answer:

\((7,0)\), the time it takes to empty the water in the pool.