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.

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.
 
 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