Question

Predict the rate of change for the depth of the diver for the intervals of [3, 4], [4, 5], and [5, 6].

Answer 1

The rate of change is 1

Explanation:

Given

`\{[3, 4], [4, 5], [5, 6]\}`

Required

Predict the rate of change

Average rate of change (R) is calculated using:

`R = (f(b) - f(a))/(b - a)`

Here, we have:

`[a,f(a)] = [3,4]` and

`[b,f(b)] = [5,6]`

Substitute these values in the above equation

`R = (6 - 4)/(5 -3)`

`R = (2)/(2)`

`R = 1`

Also, check the rate of change using:

`[a,f(a)] = [3,4]` and

`[b,f(b)] = [4,5]`

The equation:
`R = (f(b) - f(a))/(b - a)` becomes

`R = (5-4)/(4-3)`

`R = (1)/(1)`

`R = 1`

Hence, the rate of change is 1