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