A tub of water is emptied at a rate of 3 gallons per minute. the equation y –12 = –3(x – 1) models the amount of water remaining, where x is time (in seconds) and y is the amount of water left (in gallons). analyze the work shown below to determine the initial amount of water. 1. solve for the y-variable. y – 12 = –3(x – 1) y – 12 = –3x 3 y = –3x 15 2. write the equation using function notation. f(x) = –3x 15

if you plot 3,12 on a graph and go move to the left one and up one untill the x axis is zero you will land on five. so the amount the tub started with is 15

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calculista calculista · Answer 2 · 2018-08-03T10:12:17-04:00

Let

x-------> is the time in seconds

y------> is the amount of water left in gallons

we have

\(y -12 = -3(x - 1)\)

solve for y

\(y -12 = -3x+3\)

Add \(12\) to both sides

\(y -12+12 = -3x+3+12\)

\(y = -3x+15\)

\(f(x) = -3x+15\) ------> function notation

we know that

The initial amount of water is for \(x=0\)

So

substitute the value \(x=0\) in the function

\(f(x) = -3x+15\)

\(f(0) = -3*0+15\)

\(f(0) = 15 gal\)

therefore

the answer is

The initial amount of water is \(15 gal\)