the equation ( h(t)=-16 t^{2}-7 t + 3000 ) gives the height of an object that was thrown downward at 7…

the equation ( h(t)=-16 t^{2}-7 t + 3000 ) gives the height of an object that was thrown downward at 7 feet/second at an initial height of 3000 feet. use this equation to find the average rate of change in height (average speed) of the ball from 3 to 4 seconds? give answer as an integer or reduced fraction. the average rate of change (average speed) = ( ) ft/s question help: message instructor submit question

the equation ( h(t)=-16 t^{2}-7 t + 3000 ) gives the height of an object that was thrown downward at 7 feet/second at an initial height of 3000 feet. use this equation to find the average rate of change in height (average speed) of the ball from 3 to 4 seconds? give answer as an integer or reduced fraction. the average rate of change (average speed) = ( ) ft/s question help: message instructor submit question

Answer

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function (y = h(t)) over the interval ([a,b]) is (\frac{h(b)-h(a)}{b - a}). Here, (a = 3), (b=4), and (h(t)=-16t^{2}-7t + 3000).

Step2: Calculate (h(3))

Substitute (t = 3) into (h(t)): [ \begin{align*} h(3)&=-16\times(3)^{2}-7\times(3)+3000\ &=-16\times9-21 + 3000\ &=-144-21+3000\ &=2835 \end{align*} ]

Step3: Calculate (h(4))

Substitute (t = 4) into (h(t)): [ \begin{align*} h(4)&=-16\times(4)^{2}-7\times(4)+3000\ &=-16\times16-28 + 3000\ &=-256-28+3000\ &=2716 \end{align*} ]

Step4: Calculate the average rate of change

Use the formula (\frac{h(4)-h(3)}{4 - 3}). Substitute (h(3)=2835) and (h(4)=2716) into it: [ \begin{align*} \frac{h(4)-h(3)}{4 - 3}&=\frac{2716-2835}{1}\ &=- 119 \end{align*} ]

Answer:

(-119)