Question

Ryan conducted a 6 day study observing the effects of an organic plant food on the growth of his sprouting bean plant. He tracked these two pieces of info:

1. The amount of plant food remaining in the container after each days study.

2. The height of the plant over time.

Ryan found that the amount of plant food remaining decreased an equal amount each day. He used the entire 72 millimeters by the end of his study. Question

Determine the domain and the range for this relationship.


0≤y ≤6


0 ≤x ≤72


{0, 12, 24, 36, 48, 60, 72}


0 ≤x ≤6


{0,1,2,3,4,5,6}


{0,6,12,18,24,30}


0 ≤y ≤72

Answer 1

Domain:
`0\leq x\leq 6`

Range:
`\{0, 12, 24, 36, 48, 60, 72\}`

Explanation:

Let
`y` or
`f(x)` be equal to the amount of plant food that remains after each day.

`x` be the number of days that have passed.

Total amount of plant food used is 72 mm.

Number of days the experiment goes on is 6 days.

Plant food used each day is
`(72)/(6)=12\ \text{mm}`.

So, the function will be

`y=f(x)=72-12x`

at

`x=0,y=72`

`x=1,y=72-12* 1=60`

`x=2,y=72-12* 2=48`

`x=3,72-12* 3=36`

`x=4,72-12* 4=24`

`x=5,72-12* 5=12`

`x=6,72-12* 6=0`

Value of
`x` is the domain which is
`0\leq x\leq 6`.

Value of
`y=f(x)` is the range which is
`\{0, 12, 24, 36, 48, 60, 72\}`.