Question

the height in feet, h, of a model rocket t seconds after launch is given by the equation h(t)=3 + 70t - 16t^2. the average rate of change in h(t) between t = 1 second and t = 3 second is 6. what does the average rate of change tell you about the rocket? the rocket is 6 feet higher above the ground when t = 3 than it is when t = 1. the rocket is traveling six times as fast when t = 3 than it is when t = 1. the rocket is at a greater height when t = 3 than it is when t = 1. the rocket is traveling at a constant rate of 6 feet per second between t = 1 and t = 3.

Explanation:

The average rate of change of a function over an interval represents the average speed of change of the function's output (in this case, the height of the rocket) with respect to the input (time). An average rate of change of 6 for the height - time function of the rocket between \(t = 1\) and \(t=3\) means that, on average, the rocket's height is changing at a rate of 6 feet per second over that time interval.

Answer:

The rocket is traveling at a constant rate of 6 feet per second between \(t = 1\) and \(t = 3\).