Question

An arrow is shot up in the air from a height of 3 feet. The height of the arrow, in feet,can be modeled with the function h= -2t^2+12t+3where his the height in feet and is the time in seconds.Enter the average rate of change, in feet per second, from 1 second to 4 seconds

Answer 1

The average rate of change is two feet per second.

Explanation:

The height of an arrow shot up into the air from a height of three feet is given by the function:

`h(t)=-2t^2+12t+3`

And we want to find its average rate of change from one second the four seconds.

The average rate of change is synonymous with the slope. Therefore, we can evaluate the height of the arrow after the first and fourth seconds, and find the slope between them.

After the first second, the height of the arrow is:

`h(1)=-2(1)^2+12(1)+3=13`

And after the fourth second, the height of the arrow is:

`h(4)=-2(4)^2+12(4)+3=19`

This yields two points: (1, 13) and (4, 19).

The slope between them is:

`\displaystyle m=(19-13)/(4-1)=(6)/(3)=2`

Therefore, the average rate of change from one second to four seconds is two feet per second.