Question

this table displays the height of water as a pool is being filled.
use the table to interpret the rate of change.
what is the change for each consecutive input?
what is the change for each consecutive output?
what is the rate of change for the relationship?

Explanation:

Step1: Find the change for each consecutive input

The consecutive inputs (time) are \(10\), \(11\), \(12\), \(13\).
The change between \(11 - 10=1\), \(12 - 11 = 1\), \(13 - 12=1\).

Step2: Find the change for each consecutive output

The consecutive outputs (height) are \(3.75\), \(4.1\), \(4.45\), \(4.8\).
\(4.1-3.75 = 0.35\), \(4.45 - 4.1=0.35\), \(4.8 - 4.45=0.35\)

Step3: Find the rate of change

The rate of change formula is \(\text{Rate of change}=\frac{\text{Change in output}}{\text{Change in input}}\)
Since change in output \(= 0.35\) and change in input \(=1\)
\(\text{Rate of change}=\frac{0.35}{1}=0.35\)

Answer:

Change for each consecutive input: \(1\)
Change for each consecutive output: \(0.35\)
Rate of change for the relationship: \(0.35\)