Question

Melissa launches a rocket from a 3-meter-tall platform. The height, h, of the rocket, in meters, can be modeled by the given graph.

Melissa knows that h(1) = 23 meters and h(a) = 34.25 meters.

What is a reasonable estimate of the average rate of change of the height of the rocket, in meters per second, between a and b seconds? Explain your reasoning.

Answer 1

We can model the function between a and b as a linear function of negative slope because it is a short interval and the change is not very significant.
 We have then that the average rate of change in that interval is:
 m = (f (a) - f (b)) / (a-b)
 Substituting the values:
 m = (34.25 - 26) / (2.5-3.6)
 m = -7.5
 Negative, because the function decreases in that interval.
 Answer:
 a reasonable estimate of the average rate of change of the height of the rocket, in meters per second, between a and b seconds is:
 m = -7.5 m / s

Answer 2

The average rate of change of a function is the slope of the function.

The average rate of change between points a and b is -6.14 m/s

The given parameters are:

h(1) = 23

h(a) = 34.25

h(b) = 27.5

The average rate of change between points a and b is then calculated as:

$m = \frac{h(b) - h(a)}{b - a}$

So, we have:

$m = \frac{27.5 - 34.25}{b - a}$

From the figure,

a = 2.5 and b = 3.6

So, we have:

$m = \frac{27.5 - 34.25}{3.6 - 2.5}$

$m = \frac{-6.75}{1.1}$

Evaluate

$m = -6.14$

Hence, the average rate of change between points a and b is -6.14 m/s

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