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

Answer:

The rate of change is 1

Step-by-step explanation:

Given

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

Required

Predict the rate of change

Average rate of change (R) is calculated using:

$R = \frac{f(b) - f(a)}{b - a}$

Here, we have:

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

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

Substitute these values in the above equation

$R = \frac{6 - 4}{5 -3}$

$R = \frac{2}{2}$

$R = 1$

Also, check the rate of change using:

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

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

The equation: $R = \frac{f(b) - f(a)}{b - a}$ becomes

$R = \frac{5-4}{4-3}$

$R = \frac{1}{1}$

$R = 1$

Hence, the rate of change is 1