Question

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

Answer 1

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

Answer 2

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`