Determine the net change and average rate of change between the values of the variable

Question

A function is given.

h(t) = t² + 4t;     t = −1, t = 4

(a) Determine the net change between the given values of the variable.

(b) Determine the average rate of change between the given values of the variable.

Answer 1

Hello, Nick,

The first step is to calculate the values of h(t) for the two vales of t.

The net change is thus 28.

The rate of change between these two points is the slope, or rise over the run, between these two point. Since this is a non-linear function, the slope is always changing, so this would more accurately be called the average rate of change for two points.

The rise (h) is 32-(-3), or 35.

The run(t) is 4 - (-1), or 5

The rate of change (slope) is therefore 35/5 or 7 h/t. (the height changes by 7 for every increment of t, just for this section of the equation.

I hope this helps,

Bob