Q:

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)0 351 302 253 204 15Find 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

Accepted Solution

A:
Answer:AStep-by-step explanation:You are given the table[tex]\begin{array}{cc}\text{Time}&\text{Water}\\x&f(x)\\0&35\\1&30\\2&25\\3&20\\4&15\end{array}[/tex]This table represents a linear relationship between time and water leaked, because[tex]\dfrac{30-35}{1-0}=\dfrac{25-30}{2-1}=\dfrac{20-25}{3-2}=\dfrac{15-20}{4-3}[/tex]The linear function has the equation[tex]f(x)=mx+b[/tex]Find m and b:[tex]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[/tex]So,[tex]f(x)=-5x+35[/tex]Find the x-intercept:[tex]f(x)=0\Rightarrow -5x+35=0\\ \\5x=35\\ \\x=7[/tex]Hence, point (7,0) is x-intercept with the meaning x=7 is the time it takes to empty the water in the pool