MATH SOLVE

5 months ago

Q:
# 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.

Accepted Solution

A:

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

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