Question 13 Congratulations - you have been hired by NASA as their newest engineer! On your first day at
work, you are assigned to observe the launch of a new rocket prototype. You measure the
height of the rocket for the first 30 seconds after launch by finding the distance in feet between
the ground and the top of the rocket. You record your observations in the following table.
0
10
20
30
Time (seconds)
Height of Rocket
Prototype (feet)
100
922
9012
77000
A)
Determine an exponential model of the form f (z) = a b that can be used to
approximate the height of the rocket during the first 30 seconds. Show all of your work
and record your answer in the space below.
B)
Based on your exponential model, how many seconds did it take for the rocket to get
to a height of 1 mile (5280 feet)? Show all of your work and record your answer in the
Space below
Another rocket is launched the following day, and you determine that the equation
h(t) = 70.223 • (1.292) can be used to model the height, in feet, of this rockett
seconds after it has been launched. Determine the average rate of change of h(t)
over the first 5 seconds after launch. Show all work. Using correct units, explain the
meaning of your answer in the context of this problem. Show all of your work and
record your answer in the space below