Preview Activity 1.5.1.
A water balloon is tossed vertically from a fifth story window. Its height, \(h\text{,}\) in meters, at time \(t\text{,}\) in seconds, is modeled by the function
\begin{equation*}
h = q(t) = -5t^2 + 20t + 25\text{.}
\end{equation*}
(a)
Execute appropriate computations to complete both of the following tables: values of the function \(h\) on the left, average rates of change for \(h\) on the right.
| \(t\) | \(h = q(t)\) |
| \(0\) | \(q(0) = 25\) |
| \(1\) | |
| \(2\) | |
| \(3\) | |
| \(4\) | |
| \(5\) |
| \([a,b]\) | \(AV_{[a,b]}\) |
| \([0,1]\) | \(AV_{[0,1]} = 15\) m/s |
| \([1,2]\) | |
| \([2,3]\) | |
| \([3,4]\) | |
| \([4,5]\) | |
(b)
What pattern(s) do you observe in the table of function values and in the table of average rates of change?
(c)
Explain why \(h = q(t)\) is not a linear function. Use the definition of a linear function (that is, referencing average rate of change) in your response.
(d)
What is the average velocity of the water balloon in the final second before it lands? How does this value compare to the average velocity on the time interval \([4.9, 5]\text{?}\)
