Find the average rate of change in height of the orange from t=2 to t=5 (in feet per second)
The equation is h (t)=605+15t-4.9t^2 in feet.
I know the the average rate of change is change in q/ change in time. Do I put t=3 and subtract the quantity of 5 and 2 in the formula for the top?
h(5)-h(2)
-------------- = ?
5-2
To find the average rate of change in height of the orange from t=2 to t=5, you need to calculate the change in height divided by the change in time.
1. Calculate the height at t=2 and t=5:
Plug t=2 into the equation h(t) = 605 + 15t - 4.9t^2:
h(2) = 605 + 15(2) - 4.9(2^2)
= 605 + 30 - 4.9(4)
= 605 + 30 - 19.6
= 615.4 feet
Plug t=5 into the equation:
h(5) = 605 + 15(5) - 4.9(5^2)
= 605 + 75 - 4.9(25)
= 605 + 75 - 122.5
= 557.5 feet
2. Calculate the change in height:
Change in height = h(5) - h(2)
= 557.5 - 615.4
= -57.9 feet
3. Calculate the change in time:
Change in time = t(5) - t(2)
= 5 - 2
= 3 seconds
4. Calculate the average rate of change:
Average rate of change = Change in height / Change in time
= -57.9 / 3
= -19.3 feet per second
Therefore, the average rate of change in height of the orange from t=2 to t=5 is -19.3 feet per second.