2. no calculator\njacob is using his slingshot to throw peanuts out his bedroom window to feed the squirrels…

2. no calculator\njacob is using his slingshot to throw peanuts out his bedroom window to feed the squirrels in the\nwoods behind his house. the height h(t) of the peanuts can be modeled by the quadratic function\n$h(t)=-8t^{2}+20t + 14$ where height is measured in feet and time t is measured in seconds.\ndetermine the average rate of change in the height of the peanut from 1 to 3 seconds.

2. no calculator\njacob is using his slingshot to throw peanuts out his bedroom window to feed the squirrels in the\nwoods behind his house. the height h(t) of the peanuts can be modeled by the quadratic function\n$h(t)=-8t^{2}+20t + 14$ where height is measured in feet and time t is measured in seconds.\ndetermine the average rate of change in the height of the peanut from 1 to 3 seconds.

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)) over the interval ([a,b]) is (\frac{f(b)-f(a)}{b - a}). Here, (a = 1), (b=3), and (f(t)=h(t)=-8t^{2}+20t + 14).

Step2: Calculate (h(3))

Substitute (t = 3) into (h(t)): (h(3)=-8\times(3)^{2}+20\times3 + 14=-8\times9+60 + 14=-72+60 + 14 = 2)

Step3: Calculate (h(1))

Substitute (t = 1) into (h(t)): (h(1)=-8\times(1)^{2}+20\times1 + 14=-8 + 20+14=26)

Step4: Calculate the average rate of change

Using the formula (\frac{h(3)-h(1)}{3 - 1}), substitute (h(3)=2) and (h(1)=26): (\frac{2-26}{3 - 1}=\frac{-24}{2}=-12)

Answer:

The average rate of change is (-12) feet per second.