Tyreke is an engineer and needs to design a rocket for an experiment. He has calculated that the height of the rocket, in feet, with respect to time,in seconds, can be modeled by the function h(t)=-16t^2+160t. Find the average rate of change of the rocket over the interval [4,5].
To find the average rate of change of the rocket over the interval [4,5], we need to find the change in height divided by the change in time.
First, we calculate the height at t = 4:
h(4) = -16(4)^2 + 160(4) = -256 + 640 = 384 feet.
Next, we calculate the height at t = 5:
h(5) = -16(5)^2 + 160(5) = -400 + 800 = 400 feet.
The change in height over the interval [4,5] is 400 - 384 = 16 feet.
The change in time is 5 - 4 = 1 second.
Now we can find the average rate of change by dividing the change in height by the change in time:
Average rate of change = (change in height) / (change in time)
= 16 feet / 1 second
= 16 feet per second.
Therefore, the average rate of change of the rocket over the interval [4,5] is 16 feet per second.