Question

The following table shows the amount of water leaking from an inflatable pool as a function of time:

Time (in minutes)
x Water (in liters)
f(x)
0 35
1 30
2 25
3 20
4 15


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

Answer 1

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

Explanation:

0 35

1 30

2 25

3 20

4 15

5 10

6 5

7 0

The x values increase by 1 while the y values decrease by 5

So, the answer would be A (7,0) the time it takes to empty the water in the pool

Answer 2

A

Explanation:

You are given the table

`\begin{array}{cc}\text{Time}&\text{Water}\\x&f(x)\\0&35\\1&30\\2&25\\3&20\\4&15\end{array}`

This table represents a linear relationship between time and water leaked, because

`(30-35)/(1-0)=(25-30)/(2-1)=(20-25)/(3-2)=(15-20)/(4-3)`

The linear function has the equation

`f(x)=mx+b`

Find m and b:

`f(0)=35\Rightarrow 35=m\cdot 0+b,\ b=35\\ \\f(1)=30\Rightarrow 30=m\cdot 1+b,\ 30=m+35,\ m=-5`

So,

`f(x)=-5x+35`

Find the x-intercept:

`f(x)=0\Rightarrow -5x+35=0\\ \\5x=35\\ \\x=7`

Hence, point (7,0) is x-intercept with the meaning x=7 is the time it takes to empty the water in the pool