Question

Bill launched a model rocket, and estimated its height h, in feet, after t seconds. His results are shown in the table.



Time, t 0 1 2 3 4
Height, h 0 110 190 240 255

Question
Bill's data can be modeled by the function h of t equals negative 16 t squared plus 128 t.



Which value is the ,begin emphasis,best,end emphasis, prediction for the height of the rocket after 5.5 seconds?

Answer options with 5 options
A.
150 feet

B.
180 feet

C.
220 feet

D.
250 feet

E.
260 feet

Answer 1

To predict the height of the rocket after 5.5 seconds using the given model \( h(t) = -16t^2 + 128t \), we need to substitute \( t = 5.5 \) into the equation.

Calculating \( h(5.5) \):

\[
h(5.5) = -16(5.5)^2 + 128(5.5)
\]

First, calculate \( (5.5)^2 \):

\[
(5.5)^2 = 30.25
\]

Now substitute that back into the function:

\[
h(5.5) = -16(30.25) + 128(5.5)
\]

Calculating \( -16(30.25) \):

\[
-16(30.25) = -484
\]

Calculating \( 128(5.5) \):

\[
128(5.5) = 704
\]

Now combine the results:

\[
h(5.5) = -484 + 704 = 220
\]

So, the predicted height of the rocket after 5.5 seconds is **220 feet**.

**The best prediction for the height of the rocket after 5.5 seconds is: C. 220 feet.**