a rocket is launched straight up from the top of a 30 - foot tall building with an initial speed of 91 feet…

a rocket is launched straight up from the top of a 30 - foot tall building with an initial speed of 91 feet per second. the height h(t) of the rocket can be modeled by the quadratic function h(t)=-16t² + 91t + 30, where height is measured in feet and time t is measured in seconds. which statement best describes the average rate of change in the height of the rocket from 1 to 3 seconds? 18 feet per second 27 feet per second 54 feet per second 91 feet per second

a rocket is launched straight up from the top of a 30 - foot tall building with an initial speed of 91 feet per second. the height h(t) of the rocket can be modeled by the quadratic function h(t)=-16t² + 91t + 30, where height is measured in feet and time t is measured in seconds. which statement best describes the average rate of change in the height of the rocket from 1 to 3 seconds? 18 feet per second 27 feet per second 54 feet per second 91 feet per second

Answer

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function (y = f(x)) from (x=a) to (x = b) is (\frac{f(b)-f(a)}{b - a}). Here, (a = 1), (b=3), and (h(t)=-16t^{2}+91t + 30).

Step2: Calculate (h(1)) and (h(3))

  • For (t = 1): (h(1)=-16(1)^{2}+91(1)+30=-16 + 91+30=105)
  • For (t = 3): (h(3)=-16(3)^{2}+91(3)+30=-16\times9 + 273+30=-144+273 + 30=159)

Step3: Apply the average rate of change formula

(\frac{h(3)-h(1)}{3 - 1}=\frac{159 - 105}{2}=\frac{54}{2}=27)

Answer:

27 feet per second